The fault we see most in this area is a worn drive gear on a chain-drive opener - the plastic gear that the chain rides over strips down after enough years of use, especially on units original to houses built in the mid-1990s. The door won't lift even though the motor runs, and it sounds like the chain is slipping rather than pulling.
Second most common: safety sensor misalignment. Openers from the early-to-mid '90s got photo-eye sensors as standard equipment following the 1993 federal requirement, but the brackets holding those sensors are often the original ones, and after 20-plus years they've usually been bumped, jarred, or corroded enough to throw off the beam. The door reverses for no visible reason, or won't close at all.
Third: capacitor and logic board failures. These show up as an opener that hums but doesn't move, or one that runs the motor with no chain movement at all. It's not a universal fault, but on units this old, it's common enough that we check it early in the diagnosis rather than last.