On a door that's run since the mid-1980s without major hardware work, the first thing we check is the torsion spring winding cones and the center bearing plate - those two wear out together, and on a door this old, one is usually already cracked even if the spring itself hasn't gone yet. Cable condition is next; frayed strands near the bottom bracket are common on doors that have never had the cable replaced.
If the opener's original to the house, we test the drive gear and the capacitor before we touch the logic board, because a gear that's stripped teeth will mimic a dead board and send someone down the wrong repair path. We pull the panel seals too - on a door this age, the bottom seal has usually hardened and cracked from decades of cold-weather flexing, which lets drafts and water into the garage even when the door itself still operates fine.