<PAGE>

                                                                     EXHIBIT 4.2

                               WARRANT AGREEMENT

                   To Purchase Shares of the Common Stock of
                          Digital Insight Corporation
                Dated as of July 31, 2000 (the "Effective Date")

     WHEREAS, AnyTime Access, Inc., a California corporation ("ATA"), has
entered into a Master Lease Agreement dated as of July 18, 1996, Equipment
Schedule No. VL-3 dated as of September 26, 1997, and related Summary Equipment
Schedules (collectively, the "Leases") with Comdisco, Inc., a Delaware
corporation (the "Warrantholder"); and

     WHEREAS, ATA granted to Warrantholder, in consideration for such Leases, a
warrant to purchase shares of its Series B Preferred Stock (the "Original
Warrant") dated October 28, 1996 (the "Original Effective Date");

     WHEREAS, DIGITAL INSIGHT CORPORATION, a Delaware corporation (the
"Company") has entered into an Agreement and Plan of Merger dated as of March
30, 2000 (as subsequently amended, the "Merger Agreement") with ATA and ATA
Acquisition Corp. and has assumed all outstanding warrants of ATA pursuant to
the terms of the Merger Agreement;

     WHEREAS, the Company desires to assume the obligations of ATA under the
Original Warrant in accordance with the terms of the Merger Agreement by
granting to Warrantholder the right to purchase shares of its Common Stock;

     NOW, THEREFORE, in accordance with the terms of the Merger Agreement and in
consideration of mutual covenants and agreements contained herein, the Company
and Warrantholder agree as follows:

1  GRANT OF THE RIGHT TO PURCHASE COMMON STOCK.
   -------------------------------------------

     Pursuant to the Original Warrant and in accordance with the Merger
Agreement, in lieu of the right to purchase shares of ATA Series B Preferred
Stock as described in the Original Warrant, the Company hereby grants to the
Warrantholder the right, and the Warrantholder is entitled, upon the terms and
subject to the conditions hereinafter set forth, to subscribe to and purchase,
from the Company, 6,164 fully paid and non-assessable shares of the Company's
Common Stock ("Common Stock") at a purchase price of $25.95 per share (the
"Exercise Price").

     The number and purchase price of such shares are subject to adjustment as
provided in Section 8 hereof. For purposes of this Warrant Agreement, the term
"Common Stock" shall include, unless the context otherwise requires, the stock
and other securities and property at the time receivable upon the exercise of
this Warrant Agreement.

2  TERM OF THE WARRANT AGREEMENT.
   -----------------------------

     Except as otherwise provided for herein, the term of this Warrant Agreement
and the right to purchase Common Stock granted herein shall commence on the
Original Effective Date and shall be exercisable until July 18, 2006.
Notwithstanding the term of this Warrant Agreement fixed pursuant to the above
paragraph, the right to purchase Common Stock as granted herein shall expire, if
not previously exercised, immediately upon the closing of a merger or
consolidation of the Company with or into another corporation when the Company
is not the surviving corporation, or the sale of all or substantially all of the
Company's properties and assets to any other person (a "Merger"), provided that
Warrantholder realizes in such transaction a value for its shares equal to or
greater than $103.80 per share of Common Stock.

     The Company shall notify the Warrantholder in accordance with the terms of
8(e) hereof if a Merger is proposed, and if the Company fails to deliver such
written notice, then notwithstanding anything to the contrary in this Warrant
Agreement, the rights to purchase the Company's Common Stock shall not expire
until the Company complies with such notice provisions.  Such notice shall also
contain such details of the proposed Merger as are

                                       1
<PAGE>

reasonable in the circumstances. If the closing of the Merger does not take
place, the Company shall promptly notify the Warrantholder that such proposed
transaction has been terminated, and the Warrantholder may rescind any exercise
of its purchase rights promptly after such notice of termination of the proposed
transaction if the exercise of this Warrant Agreement occurred after the Company
notified the Warrantholder that the Merger was proposed. In the event of such
rescission, this Warrant Agreement will continue to be exercisable on the same
terms and conditions contained herein.

3  EXERCISE OF THE PURCHASE RIGHTS.
   -------------------------------

     The purchase rights set forth in this Warrant Agreement are exercisable by
the Warrantholder, in whole or in part, at any time, or from time to time, prior
to the expiration of the term set forth in Section 2 above, by tendering to the
Company at its principal office a notice of exercise in the form attached hereto
as Exhibit I (the "Notice of Exercise"), duly completed and executed.  Promptly
upon receipt of the Notice of Exercise and the payment of the purchase price in
accordance with the terms set forth below, and in no event later than twenty-one
(21) days thereafter, the Company shall issue to the Warrantholder a certificate
for the number of shares of Common Stock purchased and shall execute the
acknowledgment of exercise in the form attached hereto as Exhibit II (the
"Acknowledgment of Exercise") indicating the number of shares which remain
subject to future purchases, if any.

     The Exercise Price may be paid at the Warrantholder's election either (i)
by cash or check, or (ii) by surrender of this Warrant Agreement ("Net
Issuance") as determined below.  If the Warrantholder elects the Net Issuance
method, the Company will issue Common Stock in accordance with the following
formula:

                X       =      Y (A-B)
                               -------
                                  A

    Where:      X       =      the number of shares of Common Stock to be issued
                               to the Warrantholder.

                Y       =      the number of shares of Common Stock requested to
                               be exercised under this Warrant Agreement.

                A       =      the fair market value of one (1) share of Common
                               Stock.

                B       =      the Exercise Price.

     For purposes of the above calculation, current fair market value of Common
Stock shall mean with respect to each share of Common Stock:

          (i)       the average of the closing bid and asked prices for the
     Common Stock quoted on the NASDAQ system (or similar system) over the ten
     (10) trading day period ending one day before the day the current fair
     market value of the Common Stock is being determined; or

         (ii)       if at any time the Common Stock is not listed on any
     securities exchange or quoted in the NASDAQ system or the over the counter
     market, the highest price per share which the Company could obtain from a
     willing buyer (not a current employee or director) for shares of Common
     Stock sold by the Company, from authorized but unissued shares, as
     determined in good faith by the Company's Board of Directors, unless the
     Company shall become subject to a merger, acquisition or other
     consolidation pursuant to which the Company is not the surviving party, in
     which case the fair market value of Common Stock shall be the value
     received the holders of the Company's Common Stock pursuant to such merger
     or acquisition.

     Upon partial exercise by either cash or Net Issuance, the Company shall
promptly issue an amended Warrant Agreement representing the remaining number of
shares purchasable hereunder.  All other terms and conditions of such amended
Warrant Agreement shall be identical to those contained herein, including, but
not limited to the Effective Date hereof.

4  RESERVATION OF SHARES.
   ---------------------

                                       2
<PAGE>

          (a)  Authorization and Reservation of Shares. During the term of this
               ---------------------------------------
     Warrant Agreement, the Company will at all times have authorized and
     reserved a sufficient number of shares of its Common Stock to provide for
     the exercise of the rights to purchase Common Stock as provided for herein.


          (b)  Registration or Listing. If any shares of Common Stock required
               -----------------------
     to be reserved hereunder require registration with or approval of any
     governmental authority under any Federal or state law (other than any
     registration under the Securities Act of 1933, as then in effect, or any
     similar Federal statute then enforced, or any state securities law,
     required by reason of any transfer involved), or listing on any domestic
     securities exchange, before such shares may be issued, the Company will, at
     its expense and as expeditiously as possible, use its best efforts to cause
     such shares to be duly registered, listed or approved for listing on such
     domestic securities exchange, as the case may be.

     5  NO FRACTIONAL SHARES OR SCRIP.
        -----------------------------

          No fractional shares or scrip representing fractional shares shall be
     issued upon the exercise of this Warrant Agreement, but in lieu of such
     fractional shares the Company shall make a cash payment therefor upon the
     basis of the Exercise Price then in effect.

     6  NO RIGHTS AS SHAREHOLDER.
        ------------------------

          This Warrant Agreement does not entitle the Warrantholder to any
     voting rights or other rights as a shareholder of the Company prior to the
     exercise of this Warrant Agreement.

     7  WARRANTHOLDER REGISTRY.
        ----------------------

          The Company shall maintain a registry showing the name and address of
     the registered holder of this Warrant Agreement.

     8  ADJUSTMENT RIGHTS.
        -----------------

          The purchase price per share and the number of shares of Common Stock
     purchasable hereunder are subject to adjustment, as follows:

          (a)  Merger and Sale of Assets. If at any time there shall be a
               -------------------------
     capital reorganization of the shares of the Company's stock (other than a
     combination, reclassification, exchange or subdivision of shares otherwise
     provided for herein), or a merger or consolidation of the Company with or
     into another corporation whether or not the Company is the surviving
     corporation, or the sale of all or substantially all of the Company's
     properties and assets to any other person (hereinafter referred to as a
     "Merger Event"), then, as a part of such Merger Event, lawful provision
     shall be made so that the Warrantholder shall thereafter be entitled to
     receive, upon exercise of this Warrant Agreement, the number of shares of
     preferred stock or other securities of the successor corporation resulting
     from such Merger Event equivalent in value to that which would have been
     issuable if Warrantholder had exercised this Warrant immediately prior to
     the Merger Event. In any such case, appropriate adjustment (as determined
     in good faith by the Company's Board of Directors) shall be made in the
     application of the provisions of this Warrant Agreement with respect to the
     rights and interest of the Warrantholder after the Merger Event to the end
     that the provisions of this Warrant Agreement (including adjustments of the
     Exercise Price and number of shares of Common Stock purchasable) shall be
     applicable to the greatest extent possible.

          (b)  Reclassification of Shares.  If the Company at any time shall, by
               --------------------------
     combination, reclassification exchange or subdivision of securities or
     otherwise, change any of the securities as to which purchase rights under
     this Warrant Agreement exist into the same or a different number of
     securities of any other class or classes, this Warrant Agreement shall
     thereafter represent the right to acquire such number and kind of
     securities as would have been issuable as the result of such change with
     respect to the securities which were subject to the purchase rights under
     this Warrant Agreement immediately prior to such combination,
     reclassification, exchange, subdivision or other change.

                                       3
<PAGE>

          (c)  Subdivision or Combination of Shares. If the Company at any time
               ------------------------------------
     shall combine or subdivide its Common Stock, the Exercise Price shall be
     proportionately decreased in the case of a subdivision, or proportionately
     increased in the case of a combination.

          (d)  Stock Dividends. If the Company at any time shall pay a dividend
               ---------------
     payable in, or make any other distribution (except any distribution
     specifically provided for in the foregoing subsections (a) or (b)) of the
     Common Stock, then the Exercise Price shall be adjusted, from and after the
     record date of such dividend or distribution, to that price determined by
     multiplying the Exercise Price in effect immediately prior to such record
     date by a fraction, (i) the numerator of which shall be the total number of
     all shares of the Common Stock outstanding immediately prior to such
     dividend or distribution, and (ii) the denominator of which shall be the
     total number of all shares of the Common Stock outstanding immediately
     after such dividend or distribution. The Warrantholder shall thereafter be
     entitled to purchase, at the Exercise Price resulting from such adjustment,
     the number of shares of Common Stock (calculated to the nearest whole
     share) obtained by multiplying the Exercise Price in effect immediately
     prior to such adjustment by the number of shares of Common Stock issuable
     upon the exercise hereof immediately prior to such adjustment and dividing
     the product thereof by the Exercise Price resulting from such adjustment.

          (e)  Notice of Adjustments. If: (i) the Company shall declare any
               ---------------------
     dividend or distribution uponthe Common Stock, whether in cash, property,
     stock or other securities; (ii) there shall be any Merger Event; (iii)
     there shall be a public offering; or (iv) there shall be any voluntary
     dissolution, liquidation or winding up of the Company; then, in connection
     with each such event, the Company shall send to the Warrantholder: (A) at
     least twenty (20) days' prior written notice of the date on which the books
     of the Company shall close or a record shall be taken for such dividend,
     distribution, or for determining rights to vote in respect of such Merger
     Event, dissolution, liquidation or winding up; (B) in the case of any such
     Merger Event, dissolution, liquidation or winding up, at least twenty (20)
     days' prior written notice of the date when the same shall take place (and
     specifying the date on which the holders of Common Stock shall be entitled
     to exchange their Common Stock for securities or other property deliverable
     upon such Merger Event, dissolution, liquidation or winding up); and (C) in
     the case of a public offering, at least twenty (20) days written notice
     prior to the effective date thereof.

          Each such written notice shall set forth, in reasonable detail, (i)
     the event requiring the adjustment, (ii) the amount of the adjustment,
     (iii) the method by which such adjustment was calculated, (iv) the adjusted
     Exercise Price, and (v) the number of shares subject to purchase hereunder
     after giving effect to such adjustment, and shall be given by first class
     mail, postage prepaid, addressed to the Warrantholder, at the address as
     shown on the books of the Company.

          (f)  Timely Notice.  Failure to timely provide such notice required by
               -------------
     subsection (e) above shall entitle Warrantholder to retain the benefit of
     the applicable notice period notwithstanding anything to the contrary
     contained in any insufficient notice received by Warrantholder.  The notice
     period shall begin on the date Warrantholder actually receives a written
     notice containing all the information specified above.

     9  REPRESENTATIONS, WARRANTIES AND COVENANTS OF THE COMPANY.
        --------------------------------------------------------

          (a)  Reservation of Common Stock. The Common Stock issuable upon
               ---------------------------
     exercise of the Warrantholder's rights has been duly and validly reserved
     and, when issued in accordance with the provisions of this Warrant
     Agreement, will be validly issued, fully paid and non-assessable, and will
     be free of any taxes, liens, charges or encumbrances of any nature
     whatsoever; provided, however, that the Common Stock issuable pursuant to
                 --------  -------
     this Warrant Agreement may be subject to restrictions on transfer under
     state and/or Federal securities laws. The Company has made available to the
     Warrantholder true, correct and complete copies of its Certificate of
     Incorporation and Bylaws, as amended. The issuance of certificates for
     shares of Common Stock upon exercise of the Warrant Agreement shall be made
     without charge to the Warrantholder for any issuance tax in respect
     thereof, or other cost incurred by the Company in connection with such
     exercise and the related issuance of shares of Common Stock. The Company
     shall not be required to pay any tax which may be payable in respect of any
     transfer involved and the issuance and delivery of any certificate in a
     name other than that of the Warrantholder.

          (b)  Due Authority. The execution and delivery by the Company of this
               -------------
     Warrant Agreement and the performance of all obligations of the Company
     hereunder, including the issuance to Warrantholder of the right to acquire
     the shares of Common Stock have been duly authorized by all necessary
     corporate action on the part of the Company, are not inconsistent with the
     Company's Certificate of Incorporation or Bylaws, do not contravene any

                                       4
<PAGE>

     law or governmental rule, regulation or order applicable to the Company, do
     not and will not contravene any provision of, or constitute a default
     under, any indenture, mortgage, contract or other instrument to which the
     Company is a party or by which the Company is bound. This Warrant Agreement
     constitutes a legal, valid and binding agreement of the Company,
     enforceable against the Company in accordance with its terms.

          (c)  Consents and Approvals. No consent or approval of, giving of
               --------------
     notice to, registration with, or taking of any other action in respect of
     any state, Federal or other governmental authority or agency is required
     with respect to the execution, delivery and performance by the Company of
     its obligations under this Warrant Agreement, except for applicable
     requirements, if any, of the Securities Act of 1933, the Securities
     Exchange Act of 1934, Blue Sky Laws, the pre-merger notification
     requirements of the Hart-Scott-Rodino Antitrust Improvements Act, the rules
     and regulations of NASDAQ, and the filing of the Merger Agreement and
     related documents as required by the California General Corporation Law.

          (d)  Insurance.  The Company has in full force and effect insurance
               ---------
     policies, with extended coverage, insuring the Company and its property and
     business against such losses and risks, and in such amounts, as are
     customary for corporations engaged in a similar business and similarly
     situated and as otherwise may be required pursuant to the terms of any
     other contract or agreement.

          (e)  Other Commitments to Register Securities. Except as set forth in
               ----------------------------------------
     this Warrant Agreement, the Third Amended & Restated Rights Agreement dated
     February 10, 2000, among the Company and the persons named therein, and the
     Shareholder Agreement dated May 13, 1998, among nFront Inc. (a wholly-owned
     subsidiary of the Company) and the persons named therein, the Company is
     not, pursuant to the terms of any other agreement currently in existence,
     under any obligation to register under the Securities Act of 1933 any of
     its presently outstanding securities or any of its securities which may
     hereafter be issued.

     10  TRANSFERS.  This Warrant Agreement and all rights hereunder are
         ---------
     transferable in whole or in part by the Warrantholder and any successor
     transferee who agrees to be bound by the terms of this Warrant Agreement;
     provided, however, in no event shall the number of transfers of the rights
     --------  -------
     and interests in all of the Warrant Agreement exceed three (3) transfers.
     The transfer shall be recorded on the books of the Company upon receipt by
     the Company at its principal offices of a notice of transfer in the form
     attached hereto as Exhibit III (the "Transfer Notice"), and the payment to
     the Company of all transfer taxes and other governmental charges imposed on
     such transfer.

     11  MISCELLANEOUS.
         -------------

          (a)  Effective Date. The provisions of this Warrant Agreement shall be
               --------------
     construed and shall be given effect in all respects as if it had been
     executed and delivered by the Company on the date hereof. This Warrant
     Agreement shall be binding upon any successors or assigns of the Company.

          (b)  Attorneys' Fees. In any litigation, arbitration or court
               ---------------
     proceeding between the Company and the Warrantholder relating hereto, the
     prevailing party shall be entitled to attorneys' fees and expenses and all
     costs of proceedings incurred in enforcing this Warrant Agreement.

          (c)  Governing Law. This Warrant Agreement shall be governed by and
               -------------
     construed for all purposes under and in accordance with the laws of the
     State of California.

          (d)  Counterparts. This Warrant Agreement may be executed in two (2)
               ------------
     or more counterparts, each of which shall be deemed an original, but all of
     which together shall constitute one (1) and the same instrument.

          (e)  Notices.  Any notice required or permitted hereunder shall be
               -------
     given in writing and shall be deemed effectively given upon personal
     delivery, facsimile transmission (provided that the original is sent by
     personal delivery or mail as hereinafter set forth) or seven (7) days after
     deposit in the United States mail, by registered or certified mail,
     addressed (i) to the Warrantholder at 6111 North River Road, Rosemont,
     Illinois 60018, attention: James Labe, Venture Group, cc: Legal Department,
     attn: General Counsel, (and/or, if by facsimile, (847) 518-5465 and (847)
     518-5088) and (ii) to the Company at 26025 Mureau Road, Calabasas,
     California 91302, attention: Kevin McDonnell (and/or if by facsimile, (818)
     871-7555) or at such other address as any such party may subsequently
     designate by written notice to the other party.

                                       5
<PAGE>

          (f)  Remedies. In the event of any default hereunder, the non-
               --------
     defaulting party may proceed to protect and enforce its rights either by
     suit in equity and/or by action at law, including but not limited to an
     action for damages as a result of any such default, and/or an action for
     specific performance for any default where Warrantholder will not have an
     adequate remedy at law and where damages will not be readily ascertainable.
     The Company expressly agrees that it shall not oppose an application by the
     Warrantholder or any other person entitled to the benefit of this Warrant
     Agreement requiring specific performance of any or all provisions hereof or
     enjoining the Company from continuing to commit any such breach of this
     Warrant Agreement.

          (g)  No Impairment of Rights. The Company will not, by amendment of
               -----------------------
     its Certificate of Incorporation or through any other means, avoid or seek
     to avoid the observance or performance of any of the terms of this Warrant
     Agreement, but will at all times in good faith assist in the carrying out
     of all such terms and in the taking of all such actions as may be necessary
     or appropriate in order to protect the rights of the Warrantholder against
     impairment.

          (h)  Survival. The representations, warranties, covenants and
               --------
     conditions of the respective parties contained herein or made pursuant to
     this Warrant Agreement shall survive the execution and delivery of this
     Warrant Agreement.

          (i)  Severability. In the event any one or more of the provisions of
               ------------
     this Warrant Agreement shall for any reason be held invalid, illegal or
     unenforceable, the remaining provisions of this Warrant Agreement shall be
     unimpaired, and the invalid, illegal or unenforceable provision shall be
     replaced by a mutually acceptable valid, legal and enforceable provision,
     which comes closest to the intention of the parties underlying the invalid,
     illegal or unenforceable provision.

          (j)  Amendments. Any provision of this Warrant Agreement may be
               ----------
     amended by a written instrument signed by the Company and by the
     Warrantholder.


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                                       6
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Warrant
Agreement to be executed by their respective officers thereunto duly authorized
as of the Effective Date.



                              Company:  DIGITAL INSIGHT CORPORATION


                              By: /s/ Kevin McDonnell
                                 -------------------------------------------

                              Title: Senior Vice President, Chief Financial
                                     ---------------------------------------
                                     Officer and Secretary
                                     ---------------------

                              Warrantholder:  COMDISCO, INC

                              By: /s/ Jill C. Hanses
                                 -------------------------------------------

                              Title: Senior Vice President
                                     ---------------------------------------

                                       7
<PAGE>

                                   EXHIBIT I

                               NOTICE OF EXERCISE


To: _________________________

(1)  The undersigned Warrantholder hereby elects to purchase _______ shares of
     the Common Stock of Digital Insight Corporation, pursuant to the terms of
     the Warrant Agreement dated the 31/st/ day of July, 2000 (the "Warrant
     Agreement") between Digital Insight Corporation and the Warrantholder, and
     tenders herewith payment of the purchase price for such shares in full,
     together with all applicable transfer taxes, if any.

(2)  Please issue a certificate or certificates representing said shares of
     Common Stock in the name of the undersigned or in such other name as is
     specified below.


______________________________________
(Name)


______________________________________
(Address)



Warrantholder: COMDISCO, INC.

By: __________________________________

Title: _______________________________

Date: ________________________________

                                       8
<PAGE>

                                  EXHIBIT II

                          ACKNOWLEDGEMENT OF EXERCISE


          The undersigned __________________, hereby acknowledges receipt of the
"Notice of Exercise" from Comdisco, Inc., to purchase ____ shares of the Common
Stock of Digital Insight Corporation, pursuant to the terms of the Warrant
Agreement, dated the 31/st/ day of July, 2000 (the "Warrant Agreement"), and
further acknowledges that ______ shares remain subject to purchase under the
terms of the Warrant Agreement.

                                    Company:


                                    By: ______________________________________

                                    Title: ___________________________________

                                    Date: ____________________________________

                                       9
<PAGE>

                                  EXHIBIT III

                                TRANSFER NOTICE

     (To transfer or assign the foregoing Warrant Agreement, execute this form
     and supply required information.  Do not use this form to purchase shares.)

     FOR VALUE RECEIVED, the foregoing Warrant Agreement and all rights
evidenced thereby are hereby transferred and assigned to

______________________________________
Please Print Name of Transferee)


whose address is _____________________

___________________________________________

                Dated: _____________________________

                Warrantholder's Signature _________________________

                Warrantholder's Address: _______________________

                ________________________________________________


Signature Guaranteed: ______________________________________

Transferee hereby agrees to be bound by the terms and conditions of the Warrant
Agreement dated July 31, 2000 between the Company and Comdisco, Inc.

                Dated: ______________________________________

                Transferee's Signature ___________________

                Transferee's Address: ____________________

                _____________________________________________

          NOTE:  The signature to this Transfer Notice must correspond with the
                 name as it appears on the face of the Warrant Agreement,
                 without alteration or enlargement or any change whatever.
                 Officers of corporations and those acting in a fiduciary or
                 other representative capacity should file proper evidence of
                 authority to assign the foregoing Warrant Agreement.

                                       10