On units this old, the failure is rarely one clean part. A worn drive gear strips and the carriage stops catching, which looks like a dead motor but isn't. A failing capacitor makes the motor hum and try, then quit - that's an electrical fault, not a mechanical one, and swapping a gear won't fix it. Logic boards from this vintage of opener also fail outright rather than slowly; the board either fires or it doesn't, and no amount of reprogramming the remote brings it back.
Safety sensor eyes near the bottom of the track are the other common one - a knock, corrosion, or a hairline crack in the housing throws the door into a reversal loop that has nothing to do with the motor at all. We check the sensors before we touch the head unit, because it's the cheaper fix and the more common cause on older installs.