could be any number of common problems. Caps that have gone bad typically bulge, discolor, and sometimes leak. A winding could have an open circuit, or it may be that the motor is old and the brushes finally gave way.
Yes, you could hear the motor hum, but not start.
Second thing I would check is bearings. Does the shaft turn easily? If it's binding, that could also cause it to overheat. A 28 year old pump, my first guess would be bearings.
Third, could be a dead spot in the windings. If the motor spins easy and fine, maybe it stopped at a dead spot. Spinning the impeller and trying to restart it would diagnosis it.
If anyone on the forum has experience.
I just replaced a 28-year-old Grundfos UP26-99F 230V A/C water cooled pump that runs the ground loop in one of our geothermal systems and it's running fine now. I'll skip the whole troubleshooting experience and just ask my question.
The broken pump symptom was that the motor case got really hot, and the impeller wasn't turning. I pulled the external motor 'casing' off to reveal the internal 'cartridge' and its shaft that drives the impeller, and it wasn't mechanically jammed. That pump has a startup capacitor. If the startup capacitor was bad, would that cause the motor to overheat and not turn?
I don't have that much A/C motor experience. I previously replaced the startup capacitor for one of the compressors in our (previously replaced) geothermal heat pumps, but the only symptom there was the compressor simply wouldn't start. So, my thought was if the startup capacitor failed, this motor simply wouldn't turn. The fact that it got very hot very quickly made me conclude something in the motor internals had failed.
I shall attend any voice of experience that chimes in.