A little more info here would be great!
First off, before the start cap was replaced and the motor's rotor would remain in stall [not turning], was the hum very light, or was it a growling loud and scarry hum?
- Light hum = no start winding connection, either capacitor fried open, or start switch not closing... motor can remain energized for eons without problems;
- Bad hum = start / aux circuit in tact with semi or fully shorted capacitor... motor heats up and either trips breaker or thermal O/L on frame.
Secondly, what HP is this motor? Is it large enough to run the pump?
Third, is the rotor [shaft] able to spin freely? Can you hold it at start? If so, try spinning it in the opposite direction.
Fourth, how fast is the motor spinning when you are able to bring it back to locked rotor [stall] by placing your foot on the pulley?
Looking at the start switch not opening problem as mentioned by others.
This would also cause the motor to make the "Starting" sound constantly, plus become excessively hot and trip OCPD / O/L.
Lastly, is this motor multi pole - meaning less than 3450 RPMs - more like 1725 RPMs? If so, make sure all stator coils are connected as they should be.
Good luck. Let us know of the outcome.