Came home from trip, AC not working on one of three units. Went outside and fan motor was hot, but not turning. I turned off power to the unit for 30 minutes. Went back out and turned on power. Fan hummed, but did not turn. I used a wooden paint stick and gave the blades a little push and the unit roared to life.

However, the compressor doesn't seem to kick it. I assume that the outside unit's capacitor needs to be replaced since the fan needed a kick start, but does this have any bearing on the action or inaction of the compressor to start up? If not, then besides replacing the capacitor, what else should I check before calling in an experienced service tech?

It depends. If the fan was off and that caused the compressor to go off on the overheat internal overload then the fan not running could have caused the compressor not to run.

Make sure the compressor is completely cool to the touch and start the unit again. If the fan will run but not the compressor then you might get lucky and replace the combo capacitor which could be the problem with the fan and the compressor. Get the exact MFD replacement which will probably be dual rated unless the fan motor capacitor has been replaced before. One side and the common terminal will be for the fan motor and the other side and common will be for the compressor.

This is something you can do and if it works great if not then it may be time to call in a pro for a on site inspection. Do not forget to turn the power off first before servicing the unit or you might get the shock of your life knocked out of you if you know what I mean.

Hvac1000 gave you very good advice.

If this does not work let him know, because there is one other thing you can try and that is a hard start kit for you compresor.

Well, I opened it up and sure enough the capacitor looked like a coke can that had been left out in 105 degree heat all day. I grabbed a capacitor at W.W. Grainger and was back up in no time. Was concerned for a few minutes because it didn't start right up, but apparently there was a time delay on the thermostat when I turned it back on. Everything seems fine. Thanks for the advice, gentlemen,

No problem glad to help.