If the opener hums but the door doesn't move, that's almost always the capacitor or the drive gear, and neither is a job that rewards guesswork on a unit this age - parts for a chain-drive opener from the early 80s aren't sitting on a shelf at the hardware store, and ordering the wrong gear kit twice costs more than the call would have.
What you can check yourself: the wall switch wiring at the terminals (mice and time both chew at these), the sensor eyes near the floor (a spiderweb or a shifted bracket blinks the light and refuses to close the door), and whether the remote's battery is the actual problem versus the receiver inside the unit. If the opener runs the gear but the chain or belt doesn't advance, stop running it - that's a stripped gear, and continuing to cycle it just turns a $40 part into a cracked housing you now have to replace whole.