| New York State is one of those States that I have dealt with with respect to filing delinquent corporate tax returns. They are very persistent in requiring these tax returns to be filed and they have required all delinquent minimum corporation taxes to be paid along with all interest and late filing penalties.
My suggestion is file all the delinquent tax returns and pay the minimum corporation taxes and then dissolve the inactive corporation. You cannot dissolve the inactive corporations without filing the delinquent tax returns and paying all the outstanding corporation minimum taxes for NY State.
You are right in that there is no federal corporation tax due for an inactive corporation. Thus, your only tax liability will be the NY State corporation taxes along with the interest and late filing penalties (which perhaps you can request an abatement of penalties based on a valid reason for not filing the tax returns) | 
