I don't know what your problem was, but antique weapons (manufactured before 1898, or replicas of same...even in Canada) are not considered "firearms" for purposes of the NFA or GCA68 per federal law.
That said, some states see it differently. While you may not be in violation of Federal law, you may be in violation of state law. Much more hazardus to your freedom IMHO.
It is very possible (depending on your "felony") to get the record expunged and receive your civil rights back (like voting rights too). Sometimes you can do this yourself, but it normally takes a lawyer. look in your state law, Probably in the firearms laws, may be elsewhere, how to get your civil rights back.
In WA state it is in RCW 9.41.040 and 9.41.047 if you want to see a representitave example of that type of law. As long as it was not a violent felony, I would think you can probably find relief in your local state laws.
It Spokane County you file this:
http://www.spokanecounty.org/loaddoc.aspx?docid=2401 Can be done without a lawyer. One copy to the superior court, one copy to the prosecutor (good Idea to talk to the prosecutor first to see if he will fight it), and keep a copy of everything,
While I have never filed one of these for myself, I do know they work.