When I was 18 I broke the law, was convicted and had to pay restitution. Recently I hired a lawyer to expunge my record. I paid up front and then later was told that they could not find any flies on me. I decided to search myself. I just got a letter back from the city I was arrested in and they said that I had no files. If I decide to register to vote and/or register a gun and there is still a record, what kind of punishment would happen? I have kept the literature, where I was told that I have a clean record from the lawyer and the city I was charged in. Is here any other way to see if I can find my records? I am thinking that since it was from so long ago (32 years ago) that the records might have been deleted. Probably a bad assumption. I just don't know what else to do.
It's not clear which "they" reported having no records, but you need to check with the court that convicted you. The police often destroy records decades before the courts will.
Even if the court has no such record, I would be concerned about a record of your conviction existing in the national databases like NCIC. To address that, I would file a motion to expunge your conviction and then either get an order saying that the motion was granted, or that there is no conviction to expunge. I wouldn't rely on anything other than a court order.
Until then, my instinct would be to simply answer honestly any questions put to you when registering as a voter or firearm owner. I don't believe it's illegal to submit an application when you have a criminal record, though I'm confident it would be illegal to lie on the application. (The actual answer to this question would depend on your jurisdiction, which you haven't provided. You should consult a lawyer to get a reliable answer.)
It also occurs to me that you may simply be mistaken in believing that you were convicted. Frequently, courts will allow someone to enter some kind of conditional plea but refrain from entering a conviction if they behave themselves or meet some other criteria. If the court is satisfied with the defendant's performance, the charges may be dismissed altogether and eventually automatically expunged.