<PAGE>   1
                                                                   EXHIBIT 10.34

                                                                     EXHIBIT A-1


                         LIMITED (OVERADVANCE) GUARANTEE

            LIMITED (OVERADVANCE) GUARANTEE dated as of September __, 1996 made
by WELSH, CARSON, ANDERSON & STOWE VII, L.P. ("WCAS VII") and WCAS CAPITAL
PARTNERS II, L.P ("WCAS CP II") (each a "Guarantor", and collectively, the
"Guarantors") in favor of THE CHASE MANHATTAN BANK (formerly known as Chemical
Bank), a New York banking corporation, as agent (the "Agent") for (i) the
lenders (the "Lenders") named in the Credit Agreement dated as of March 29, 1996
among Aurora Electronics Group, Inc. (the "Borrower"), the guarantors named
therein, the Agent and the Lenders (as amended, modified, restated or
supplemented from time to time in accordance with its terms, the "Credit
Agreement"; capitalized terms used herein and not otherwise defined herein shall
have the meanings attributed thereto in the Credit Agreement) and (ii) itself as
issuer of the Letters of Credit.

            The Required Lenders have agreed to amend and waive certain
provisions of the Credit Agreement pursuant to, and subject to the terms and
conditions of, a Waiver and Amendment Agreement dated the date hereof. The
obligation of the Required Lenders to waive certain provisions of the Credit
Agreement and to amend certain provisions of the Credit Agreement is
conditioned, inter alia, on the execution and delivery by the Guarantors of a
guarantee in the form hereof to secure the due and punctual payment by the
Borrower of all Overadvance Loans, when and as due, whether at maturity, by
acceleration, upon one or more dates set for prepayment or otherwise.

            Accordingly, each of the Guarantors hereby agrees with the Agent as
follows:

            SECTION 1. Guarantee of Overadvance Loans. Each Guarantor
absolutely, irrevocably and unconditionally guarantees, severally and not
jointly, the due and punctual payment, when due, whether at maturity, by
acceleration, by notice of prepayment or otherwise, the due and punctual
performance of all Overadvance Loans; provided, however, that, notwithstanding
the foregoing, the maximum liability of the Guarantors hereunder shall not
exceed $3,000,000; provided, further, that, notwithstanding the foregoing, each
Guarantor's maximum individual liability hereunder, as at any day of
determination, shall not exceed an amount equal to such Guarantor's Fractional
Share (as hereinafter defined) of $3,000,000. Each Guarantor further agrees that
the Obligations may be amended, extended or renewed, in whole or in part,
without notice or further assent from it, and that it will remain bound upon
this Guarantee notwithstanding any amendment, extension or renewal of any
Obligation; provided, however, that no such amendment, extension or renewal
shall be deemed to increase the maximum liability hereunder of the Guarantors to
an amount in excess of $3,000,000. "Fractional Share" shall mean (i) with
respect to WCAS VII, 96.6%, and (ii) with respect to WCAS CP II, 3.4%.


<PAGE>   2
            Each Guarantor waives, upon the failure of the Borrower to pay any
Overadvance Loan when and as the same shall become due (whether at maturity, by
acceleration, after notice of prepayment or otherwise), presentation to, demand
of payment from, and protest to, the Borrower of any of the Obligations, and
also waives notice of acceptance of this Guarantee and notice of protest for
nonpayment. The obligations of each Guarantor hereunder shall not be affected by
(a) the failure of any Lender or the Agent to assert any claim or demand or to
enforce any right or remedy against the Borrower under the provisions of the
Notes, the Credit Agreement or any of the Security Documents or otherwise; (b)
any extension or renewal of any thereof; (c) any rescission, waiver, amendment
or modification of any of the terms or provisions under the Notes, the Credit
Agreement, any of the Security Documents, any guarantee or any other agreement;
(d) the release of any of the security held by the Agent for the benefit of the
Lenders for the Obligations or any of them; (e) the failure of any Lender or the
Agent to exercise any right or remedy against any other guarantor of the
Obligations; or (f) any bankruptcy, receivership or other insolvency proceeding
of the Borrower or any subsidiary thereof (and each Guarantor specifically
acknowledges that for purposes of such Guarantor's obligations under this
Guarantee interest shall continue to accrue on the Obligations in accordance
with the Credit Agreement notwithstanding any cessation of such interest
accruals imposed in any such insolvency proceeding for the benefit of the
Borrower).

            Each Guarantor further agrees that this Guarantee constitutes a
guarantee of payment when due and not of collection, and waives any right to
require that, upon the failure of the Borrower to pay any Overadvance Loan when
and as the same shall become due (whether at maturity, by acceleration, after
notice of prepayment or otherwise), any resort be had by the Agent or any Lender
to any security held for payment of Obligations which constitute all or a
portion of any Overadvance Loan or to any balance of any deposit account of
credit on the books of the Agent or any Lender in favor of the Borrower or any
other person.

            Except as expressly provided herein, the obligations of each
Guarantor hereunder shall not be subject to any reduction, limitation,
impairment or termination for any reason, including, without limitation, any
claim of waiver, release, surrender, alteration or compromise, and shall not be
subject to any defense of setoff, counterclaim, recoupment or termination
whatsoever by reason of invalidity, illegality or unenforceability of the
Obligations or otherwise. Without limiting the generality of the foregoing, the
obligations of each Guarantor hereunder shall not be discharged or impaired or
otherwise affected by the failure of the Agent or any Lender to assert, upon the
failure of the Borrower to pay any Overadvance Loan when and as the same shall
become due (whether at maturity, by acceleration, after notice of prepayment or
otherwise), any claim or demand or to enforce any remedy under the Notes, the
Credit Agreement, or under any Security Document, any guarantee or any other
agreement, by any waiver or modification of any thereof, by any default, failure
or delay, willful or otherwise, in the performance of the Obligations, or by any
other act or thing or omission or delay to do any other act or thing


                                        2
<PAGE>   3
which may or might in any manner or to any extent vary the risk of either
Guarantor or would otherwise operate as a discharge of either Guarantor as a
matter of law or equity.

            Each Guarantor further agrees that, unless this Guarantee shall have
been theretofore terminated pursuant to the express provisions hereof, this
Guarantee shall continue to be effective or be reinstated, as the case may be,
if at any time payment, or any part thereof, of principal of or interest on any
Obligation which constitutes all or a portion of any Overadvance Loan is
rescinded or must otherwise be restored by the Agent or any Lender upon the
bankruptcy or reorganization of the Borrower or otherwise.

            In furtherance of the foregoing and not in limitation of any other
right which any Lender or the Agent may have at law or in equity against the
Guarantor by virtue hereof, upon the failure of the Borrower to pay any
Obligation which constitutes all or a portion of any Overadvance Loan when and
as the same shall become due, whether at maturity, by acceleration, after notice
of prepayment or otherwise, the Guarantors, severally and not jointly, hereby
each promise to and will, upon receipt of written demand by the Agent, forthwith
pay, or cause to be paid, to the Agent for the ratable benefit of the Lenders in
cash such Guarantor's Fractional Share of the amount of such unpaid Obligations.

            Each Guarantor assumes all responsibility for being and keeping
itself informed of the financial condition and assets of Borrower and its
subsidiaries, and of all other circumstances bearing upon the risk of nonpayment
of the Overadvance Loans and the nature, scope and extent of the risks which
each Guarantor assumes hereunder, and agrees that neither the Agent nor any
Lender will have any duty to advise either Guarantor of information known to it
or any of them regarding such circumstances or risks.

            SECTION 2. Representations and Warranties. Each Guarantor represents
and warrants to the Agent that:

                        (a) Organization, Powers, etc. Each Guarantor (i) is a
limited partnership duly organized, validly existing and in good standing under
the laws of the jurisdiction of its organization, (ii) has the partnership power
to execute, deliver and perform this Guarantee and (iii) has made all requisite
filings with governmental authorities in all jurisdictions in which the
character of its properties or the nature of its business makes such filing
necessary.

                        (b) Authorization of Guarantee, etc. The execution,
delivery and performance by each Guarantor of this Guarantee and all actions
contemplated hereby (i) are duly authorized, (ii) will not violate (a) any
provision of law, of the rules or regulations thereunder, any order of any court
or other agency of government or the partnership agreement of such Guarantor or
(b) any provision of any indenture, agreement or other instrument to which such
Guarantor is a party, or by which such Guarantor or any of its properties is or
may be bound, and (iii) will not be in conflict with, result in a breach


                                        3
<PAGE>   4
of or constitute (with due notice, lapse of time or both) a default under, any
such indenture, agreement or other instrument, or result in the creation or
imposition of any lien upon any of the property or assets of the Guarantor,
except as contemplated hereby.

                        (c)   Legal, Valid and Binding Obligations, etc.  This
Guarantee is a legal, valid and binding obligation of each Guarantor,
enforceable in accordance with its terms, subject to bankruptcy, reorganization,
insolvency, moratorium and other similar laws affecting the enforcement of
creditors' rights generally and the exercise of judicial discretion in
accordance with general principles of equity.

                        (d) Status of Guarantee. The obligations of each
Guarantor hereunder will, upon demand for payment by the Agent pursuant to
Section 1 hereof, constitute direct, unconditional and general obligations of
each Guarantor and rank in right of payment pari passu with all indebtedness and
liabilities for borrowed money, or other obligations arising out of an extension
of credit, of either Guarantor. Neither Guarantor has issued any such
indebtedness or incurred any such liability or obligation which is subordinated
to any other such indebtedness, liability or obligation but which will not be
subordinated to the payment in full of any and all amounts payable hereunder.

                        (e)   Governmental Approvals.  No consent, approval,
authorization, permit or license of any Federal, state or local regulatory
authority is required in connection with the making or performance by the
Guarantors of this Guarantee and the transactions contemplated hereby.

            SECTION Subrogation. Upon (i) the indefeasible payment in full, in
cash, of all Obligations, (ii) the Lenders having no further commitment to make
any Loans under the Credit Agreement and (iii) the Agent having no further
obligation to issue any Letters of Credit, the Guarantors shall be subrogated to
the rights of the Agent and the Lenders to receive payments or distributions of
assets of the Borrower applicable to the Obligations until all amounts paid by
the Guarantors in respect of this Guarantee shall be paid in full; and, for the
purposes of such subrogation, no payment or distributions to the Agent of the
Lenders of any cash, property or securities to which the Guarantors would be
entitled except for the provisions of this Section 3 shall, as between the
Borrower, its creditors (other than the Agent and the Lenders) and the
Guarantors, be deemed a payment to or on account of the amounts paid by the
Guarantors hereunder.

            SECTION 3. Supporting Documents. In connection with the execution
and delivery of this Guarantee, each Guarantor shall deliver or cause to be
delivered to the Agent on or prior to the date hereof: (i) the favorable written
opinion of counsel for the Guarantors addressed to the Lenders and in form and
substance satisfactory to the Agent, (ii) a certificate dated the date hereof of
a general partner of its sole general partner as to the incumbency and
signatures of the general partner of such sole general partner executing this
Guarantee and any certificate or letter delivered pursuant to this Guarantee,
(iii) a certification by another general partner of the sole general partner of
each of the


                                        4
<PAGE>   5
Guarantors as to the incumbency and signature of the general partner executing
such certificate and (iv) such additional supporting documents as the Agent may
reasonably request.

            SECTION 4. Notices. All notices, demands, requests, consents or
approvals required under this Guarantee shall be in writing and shall
conclusively be deemed to have been received and to be effective on the day on
which hand delivered to the Agent at 633 Third Avenue, New York, New York, 10017
or to each Guarantor at the address set forth on the signature pages hereof, as
the case may be, or on the day which received, if sent by mail to each Guarantor
or the Agent, as the case may be, at said address.

            SECTION 5. Scope and Survival of Agreement. This Guarantee, together
with the related instruments and transactions to which reference is expressly
made herein, constitutes the entire agreement of the parties and supersedes all
prior written and oral agreements and understandings with respect hereto among
the Guarantors, the Borrower and the Agent. All covenants, agreements,
representations and warranties made herein and in the certificates or other
instruments or documents delivered pursuant hereto shall continue in full force
and effect so long as any Obligation which constitutes all or a part of any
Overadvance Loan is outstanding and unpaid; provided, however, that the
representation and warranty set forth in subparagraph (d) of Section 2 hereof
shall be deemed to be repeated on each successive day so long as any Obligation
which constitutes all or a part of any Overadvance Loan is outstanding and
unpaid. Whenever in this Guarantee reference is made to either Guarantor, the
Borrower or the Agent, such reference shall be deemed to include the successors
and assigns of such party; and all covenants, promises and agreements by or on
behalf of either Guarantor which are contained in this Guarantee shall inure to
the benefit of the successors and assigns of the Borrower and each of the
Lenders.

            SECTION 6. Setoff. In addition to and not in limitation of any
rights which the Agent may have under applicable law or otherwise, each
Guarantor authorizes the Agent to apply any credit balance of the Agent from the
Guarantor hereunder and, in the name of each Guarantor or the Agent, do all such
acts and execute all such documents as may be necessary or expedient for any
such purpose.

            SECTION 7. Modification of Agreement. No modification, amendment or
waiver of any provision of, nor any consent required by, this Guarantee, nor any
consent to any departure by either Guarantor therefrom, shall in any event be
effective unless the same shall be in writing and signed by the Agent and the
Guarantors and then such modification, amendment, waiver or consent shall be
effective only in the specific instance and for the purpose for which given. No
notice to or demand on either Guarantor in any case shall entitle such Guarantor
to any other or further notice or demand in the same, similar or other
circumstances. The holder of the Notes shall be bound by any modification,
waiver or consent authorized by this Section 8, regardless of whether the Notes
shall have been marked to indicate such consent.


                                        5
<PAGE>   6
            SECTION 8. Remedies Cumulative, etc. No right, power or remedy
herein conferred upon or reserved to the Agent is intended to be exclusive of
any right, power or remedy or remedies, and each and every right, power and
remedy of the Agent pursuant to this Guarantee or the Notes or now or hereafter
existing at law or in equity or by statute or otherwise shall, to the extent
permitted by law, be cumulative and concurrent and shall be in addition to every
other right, power or remedy pursuant to this Guarantee or the Notes or now or
hereafter existing at law or in equity or by statute or otherwise, and the
exercise or beginning of the exercise by the Agent of any one or more of such
rights, powers or remedies shall not preclude the simultaneous or later exercise
by the Agent of any or all such other rights, powers or remedies.

            SECTION 9. No Waiver, etc. No failure or delay by the Agent to
insist upon the strict performance of any term, condition, covenant or agreement
of this Guarantee or of the Notes, or to exercise any right, power or remedy
hereunder or thereunder or consequent upon a breach hereof or thereof, shall
constitute a waiver of any such term, condition, covenant, agreement, right,
power or remedy of any such breach, or preclude the Agent from exercising any
such right, power or remedy at any later time or times.

            SECTION 10. Severability. In case any one or more of the provisions
contained in this Guarantee should be invalid, illegal or unenforceable in any
respect, the validity, legality and enforceability of the remaining provisions
contained herein shall not in any way be affected or impaired thereby, and the
parties hereto agree to negotiate in good faith to replace any such invalid,
illegal or unenforceable provision with a new valid, legal and enforceable
provision that, to the extent possible, will preserve the financial bargain of
this Guarantee or to otherwise amend this Guarantee, including Section 12
hereof, to obtain such effect.

            SECTION 11. APPLICABLE LAW. THIS GUARANTEE SHALL BE GOVERNED AND
CONSTRUED IN ACCORDANCE WITH THE LAW OF THE STATE OF NEW YORK (OTHER THAN
CONFLICT OF LAWS PRINCIPLES THEREOF) AND ANY APPLICABLE LAW OF THE UNITED STATES
OF AMERICA.

            SECTION 12. Termination. This Guarantee shall terminate upon the
earlier to occur of (i) such time as the Agent shall have received financial
statements of the Borrower pursuant to Section 6.05(a) of the Credit Agreement
that demonstrate to the satisfaction of the Agent that the Loan Parties are in
compliance with the provisions of Sections 7.08, 7.09, 7.09A and 7.10 of the
Credit Agreement in effect as of the Closing Date or (ii) such time as (x) all
Obligations have been indefeasibly paid in full, in cash, (y) the Lenders have
no further commitment to make any Loans under the Credit Agreement and (z) the
Agent shall have no further obligation to issue any Letters of Credit.

            SECTION 13. Collection Expenses. Each Guarantor agrees to pay all
reasonable out-of-pocket expenses incurred by the Agent or any of the Lenders in
connection with the enforcement or protection of its rights in connection with
this


                                        6
<PAGE>   7
Guarantee, or in connection with any pending or threatened action, proceeding,
or investigation relating to the foregoing, including but not limited to the
reasonable fees and disbursements of counsel for the Agent and the Lenders.

            SECTION 14. Counterparts. This Guarantee may be executed in
counterparts, each of which shall constitute an original, but all of which shall
together constitute one and the same agreement.

            IN WITNESS WHEREOF, each Guarantor has caused this Guarantee to be
duly executed, as indicated below, by its general partner, all as of the day and
year first above written.

                            WELSH, CARSON, ANDERSON &
                                 STOWE VII, L.P.

                                    By: WCAS VII PARTNERS, its general partner


                                          By:  ________________________, a
                                                general partner
                                                Name:

                                    Address:    320 Park Avenue
                                                New York, New York 10022
                                                Attention:   Richard M. Stowe
                                                             Thomas E. McInerney

                                    WCAS CAPITAL PARTNERS II, L.P.

                                    By: WCAS CP II PARTNERS, its general partner


                                          By:  ________________________, a
                                                general partner
                                                Name:
 
                                    Address:    320 Park Avenue
                                                New York, New York 10022
                                                Attention:   Richard M. Stowe
                                                             Thomas E. McInerney



                                        7
<PAGE>   8
ACCEPTED:

THE CHASE MANHATTAN BANK, as Agent

By:_________________________________
   Name:
   Title:





                                        8