Both Yes and No. You need a more thorough review of your issue before anyone can provide you the most accurate advice, but it is possible to have your rights restored if they have been restricted.
Unfortunately the method to do that requires some extraordinary motions and intense lobbying of the state by your representative attorney. It is also a purely speculative process as your rights to appeal the conviction are long since closed.
We would be happy to set up and assist you with the process, but it is a hard road and the odds of success are stacked against you from the start. It has been done though. Just depends how much your 2nd Amendment rights mean to you.
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The first step is to get a certified copy of the docket to see what the ACTUAL finding and disposition were. It may be that NICS failed to note that, while charged with DV, you were not convicted of that charge.
If so, a NICS appeal, with that certified copy, may resolve your issue. If not, the other response lays out what needs to be done.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
I'm not sure why attorneys who aren't criminal defense attorneys are answering your question, as they are mostly incorrect. Yes, things can be fixed. Depending on exactly what happened, the way to fix it may be different. However, in no situation do you need your State legislators involved, nor a "NCIC appeal".
Please let me know if I can be of assistance. I would be happy to help.
M. Jason Rhoades