[Richard]

Is the sound you hear a loud buzz? You already said the condenser fan is not turning. Replace the start cap as you already figured out. A quick and dirty way of checking it is to start the fan spinning by hand if you can do that safely with a stick or other help. If you spin it and the fan starts and runs then almost always is the start cap. Before you remove the start cap. Turn off all power to unit and confirm with voltmeter. Then take a screwdriver and short the terminals of the cap. That will save you a nasty shock. Take a picture and draw yourself a wiring diagram. Most ac supply houses will have what you need. There are two ratings on most caps. Try to match both.