It looks like you've decided to sell your instruments. I'm not sure what program you are trying to obtain aid under, but it sounds to me like the people you are dealing with are wrong. Have you asked to see a copy of the policy that requires you to sell your guitar? At the risk of arguably going a bit off topic, let me be specific about what I meant in my earlier post.

Title 10, Chapter 90 of the New Jersey Administrative Code, governing the "Work First" program provides, at Subchapter 3, "Eligibility-- income, resources, benefits" under § 10:90-3.20, "Exempt resources" as follows:

(a) Exempt resources are not subject to any requirement for liquidation and are not considered in determining WFNJ eligibility or in determining the cash assistance benefit. In addition to the exempt income set forth at N.J.A.C. 10:90-3.19, the following resources shall be exempt for each assistance unit:
. . .
6. Personal property, such as, but not limited to, house furnishings and clothing which are used regularly or likely to be used;
    i. Furnishings and clothing in storage may be deemed to be exempt in the presence of a reasonable plan for their use;
    ii. Personal effects if regularly used or of small intrinsic value;
. . .
7. Livestock, machinery, tools, equipment, and stock-in-trade which serve to produce some net income in cash or in kind or serve as an incentive for self-help; livestock or property owned or used by a child in connection with a group or school activity (such as 4-H); and farm and garden products raised by the eligible assistance unit for its own use;

I don't know anything about public aid and I'm not a New Jersey lawyer, but if I were in your situation, I would have pointed to that regulation and claimed the guitar to be exempt both under § 10:90-3.20(a)6.ii., as a regularly used personal effect and under § 10:90-3.20(a)7. as a tool which could produce some income.

I suggest getting a copy of the regulations that affect the program that you are applying for and study them carefully. You owe it to yourself and your family to know the rules so you cam use them to your advantage. This website may help:
http://www.michie.com/newjersey/lpext.dll/uanjadmin/1/4f9b7?f=templates&fn=document-frame.htm&2.0#JD_analysis21995