Diagnosis
The pump is seized or the motor capacitor is failing under load. The hum indicates the motor is trying but cannot turn.
How to Fix It
First, disconnect power. Try to turn the pump pulley by hand. If it won't budge, the pump internals are locked up from freeze damage or sediment. The pump assembly must be replaced.
If That Didn't Work
If the pulley turns freely, the issue is likely the motor's run capacitor. It's located in the motor end cap. A bulging or leaking capacitor needs replacement.
Heads Up
Do not keep trying to start a seized pump. You will burn out the motor windings in seconds. The hum and hot smell are the final warning.