Start with the capacitor.

It’s almost always the start capacitor. That little cylinder in the back of the motor gives it the kick to get spinning. When it fails, the motor hums but doesn’t move.

Try giving the motor shaft a quick spin with a screwdriver (carefully, while power is off and then briefly back on). If it starts running, you’ve confirmed the capacitor is dead. Replace it — they’re cheap and easy to swap. Part number is usually printed on the side.

If it still hums and won’t spin even with a manual nudge, you’ve got a seized bearing or a dead winding. At that point, just buy a new pump motor. The repair cost+time isn’t worth it.

Capacitors first. That’s the fix 9 times out of 10.