<PAGE>

                                                                     EXHIBIT 4.1

                               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. (formerly known as CU Resources, Inc.), a
California corporation ("ATA"), had entered into a Master Lease Agreement dated
as of July 18, 1996, Equipment Schedule No. VL-1 dated as of July 18, 1996,
Equipment Schedule VL-2 dated as of October 28, 1996 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, dated July 18, 1996 (the "July Warrant"); and a warrant, dated October
28, 1996 (the "October Warrant" and, together with the July Warrant, the
"Original Warrants"), to purchase shares of its Series A Preferred Stock;

     WHEREAS, the "Original Effective Date" applicable to the July Warrant is
July 18, 1996, and the "Original Effective Date" applicable to the October
Warrant is October 28, 1996;

     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 Warrants 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 Warrants and in accordance with the Merger
Agreement, in lieu of the right to purchase shares of ATA Series A Preferred
Stock as described in the Original Warrants, 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, 36,761 fully paid and non-assessable shares of the Company's
Common Stock ("Common Stock") at a purchase price of $4.42 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 Dates 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

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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 $17.68 per share of Common Stock.

     The Company shall notify the Warrantholder in accordance with the terms of
8(f) 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 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 Warrants  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 Warrants ("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.

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<PAGE>

     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.
   ---------------------

     (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

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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.

     (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 upon the 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.

                                       4
<PAGE>

     (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 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 Securiites 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 Warrants
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

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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.

     (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
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                                  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, 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