The corporation is inactive but you have not filed the tax returns due. Clearly, you are required to file a tax return or at least file an inactive NJ Tax return. Leaving it active simply means that you are incurring a minimum tax liability every year!
Please refer to the following article that discusses in depth the consequences of not dissolving a NJ Corporation.
What are the consequences of not dissolving a C Corporation in State of NJ?
There typically should not be substantial fines and penalties from the IRS as you have Zero income. Unfortunately, you will need to file an Inactive return for NJ state and pay the minimum NJ corporation tax along with interest and penalties that may be due!
I would "formally dissolve your corporation" and attempt to pay prior taxes due. This is the correct approach and I would request you to contact your CPA and have him or her prepare the dissolution paperwork for you.
