3 Steps to Diagnose a Humming Motor
Check the start capacitor The small cylinder on the back of the motor gives it the initial spin. When it fails, the motor hums but does not move.
Manually spin the shaft With power off, carefully spin the motor shaft with a screwdriver, then briefly turn power on. If it starts running, the capacitor is dead. Replace it — they are cheap and the part number is printed on the side.
Replace the motor if it still hums If the motor hums and will not spin even with a manual nudge, you have a seized bearing or dead winding. Buy a new pump motor — repair is not worth the time or cost.