Rick,
I am not sure about your case but I had a capacitor go bad in my heat pump unit a couple of years ago. The symptoms weren't quite the same but it was one of the can capacitors and I could see the swelling of the can so I got it fixed before it blew. And yes, they do fail. And as big as these normally are, turn the power off and get a good cable to discharge it to ground. Or if you are in a hurry just put your fingers across the terminals. I will be watching for the first human satellite. Didn't you ever take the old capacitors out of the distributors on a points system and charge them and then just lay them down and wait until someone picked them up to watch the fun? Except the capacitors in my unit carry such a charge that no way do you want to discharge them through your body.
If you have an induction current meter and know what the motor should draw at start that would be an easy way to see if it is getting the initial high bump charge. Also make sure that even though the relay seems ok the contacts haven't burned and it isn't putting enough juice through to charge the capacitor fully. I don't know what yours would cost but my unit has two and they cost enough to buy a small car.
Ron
