How can I obtain my gun rights back if the conviction happened 35 years ago?

This is complex and you cannot get legal advice for this over the web because of the legal research involved. However, the first step is to determine whether the statute you were convicted of is a lifetime ban on possession. Step 2 would be to see if your felony could be reduced to a misdemeanor. Step 3 would be expungement which many judges would be hesitant to grant despite what is in the statute. Also it is easier to expunge a misdemeanor than a felony.