OK, I would start here
Since this is a NY corporation, NY law will apply. That is you need to comply with NY law to keep this Corporation "legal".
You will find on this page a requirement for NY Corporations
to file a "bi-annual" statement. Basically, this is a statement from the corporation to the state of NY every 2 years to document the progress of the corporation. Since there has been no activity, this should be fairly straight forward.
From the state website:
A business corporation is required by Section 408 of the Business Corporation Law to file a Biennial Statement setting forth: (a) the name and respective business address of its chief executive officer; (b) the street address of its principal executive office; and (c) the post office address within or without this state to which the Secretary of State shall mail a copy of any process against it served upon him or her.
The filing period for a corporation is the calendar month in which its original Certificate of Incorporation or Application for Authority was filed (or the effective date thereof, if stated). The Biennial Statement is made on a form provided by the Secretary of State which is automatically mailed to the most recent principal place of business on record; if none is listed, the form is mailed to the address for the Secretary of State to forward service of process. The statutory filing fee is $9. A corporation wishing to file a Biennial Statement that has not received a form may request one by phone ((518)(NNN) NNN-NNNN or in writing; the corporation's name must be included with the request.
You also need to file taxes. Again, if not income, this is simple and you would not expect to be taxed...but you need to file. If you have not yet done so, you will need an Taxpayer ID no. You can get one from www.irs.gov
SO, I suspect there will be some fees associated with this "restart" but I suspect they will be nominal.
Read through the states corporation website...then call up the state agencies that handle these matters (corporations and taxes)...I suspect this will not take too much effort