A few minor tests
My background is more electronics than mechanics, but if I were you, I'd try this:
- Take a voltmeter with some clip leads, put it on the highest setting, connect it to the motor input leads and turn down the voltage range until you see something. Is the motor getting any voltage? (Be damn careful BTW!) Use common sense and don't select anything less than 25 volts, unless you really hate your meter.
- If the motor is getting voltage, then yeah, it could be a bad cap. They generally look a bit like a pop can, usually silver in colour. They shouldn't be "Puffy" and the black portion with the terminals sticking out should be flat.
- Some multimeters have a capacitance tester on them. If possible, check the capacitance value of the motor start capacitors. They shouldn't vary anything more than 5 percent of rated value on the can.
- Examine the PCB's (Printed Circuit Board) and check for anything which may indicate a component failure. Look for scorch marks, blown capacitors or anything else that doesn't look right.
Capacitors are one of those things that tend to give out with time, unfortunately.
If you can get a service manual, sometimes PCB's will have spots marked "TP" followed by some number. This means "Test Point". You can measure voltages at test points to see if you are getting the expected output at a certain stage of the machines operation.
Good luck!