Motor hums but will not turn over - Check for a bad capacitor. You may have two: a run capacitor and a start capacitor. Some motor have a governor at the electrical end of the shaft. Check that it is not stuck open. If your capacitor(s) and governor are good and the motor shaft rotates easily you probably have a burned out motor coil and you will need to repair or replace the motor.
Motor gets hot and shuts down - Generally due to low voltage or being overloaded. Check that the motor is wired correctly. If the motor is configured for 230V and has 115V coming in, it will shut down after running 3-5 minutes. Check for loose connections. Check for undersized wiring. For a hook-up to the circuit box of under 50', pumps of up to 2HP wired for 230V need No. 14 size wire, For pumps wired for 115V, the wire size must be No. 14 for 1/2 and 3/4 HP; No 12 for 1 HP; and No. 10 for 1 1/2 and 2 HP. Check that the motor is not overloaded. Does the pump have the correct impeller and diffuser for this motor? Is the impeller worn and rubbing on the diffuser.
Note: Most pump motors have Automatic Thermal Overload Protection. The motor will automatically shut off before the motor generates enough heat to damage itself. Once a normal heat level is reached, the motor will automatically restart. CAUTION: If the motor operates in this on/off mode for any length of time it will burn out.