Two-speed hot tub motor hums but doesn't run
Many single phase motors use a start capacitor. If it fails the motor can hum without starting. Sometimes they puff up and are obviously broke. If it appears OK visually then you will need to test it.

To test a capacitor you will need to disconnect it from the motor. If not use a digital multimeter set on resistance connected across the terminals of the capacitor. Initially it should read extremely low and the resistance should climb as the capacitor charges. Reversing your leads should yield the same result. If you get these results, the capacitor is good.

Otherwise a failed capacitor will read zero or infinite resistance.

If it is not the capacitor, it could be the pump motor is seized or the piping is plugged.

Good luck!