It would seem to me that you have what is known as a net operating loss in a C corporation. This loss cannot be passed on to you as a shareholder. The net operating loss however is carried over to the next year to be available to offset the future C corporation's taxable income. The question you are asking is whether to maintain the C corporation or dissolve it!
Well, to answer your first question, "Should you dissolve your corporation?", I have to ask your whether or not you expect to earn any income or profits in the foreseeable future? If you do expect to earn profits, I do not recommend that you close the corporation until you collect this income and absorb all the net operating income.
Just because there is no activity or income in the past year or current year is not reason enough to close this corporation. You have to consider the income in the future years as well, and if you strongly believe that there is absolutely no future income guaranteed, then this would be good reason to dissolve this corporation.
The second question you have asked is "What will be minimum amount of tax that I have to pay this year if I chose to keep it alive?"The cost of keeping this corporation alive in NJ state is the annual NJ corporation tax of $520 plus the annual report of $50.
The third question you have asked, "What will be dissolving costs, if I decided to dissolve the company?"According to the New Jersey Division of Taxation, "all annual report obligations should be satisfied prior to submitting the dissolution paperwork." Generally speaking the cost of dissolving a NJ Corporation is $120.00. An experienced CPA will can handle all the paperwork for closing out the C corporation and his fees may range anywhere from $250 to $500.