AC Capacitor Or Another Problem? (And What Type Of Capacitor?)
You are probably correct on it being the capacitor.  Most time the compressor and ODM (outdoor fan motor) capacitor are combined into one.  If you can get that capacitor out (looks like a small tin can with 3 prongs coming out the top) and it looks puffy, most likely bad.  You can easily check this if you have a decent multi meter like a Fluke.  Otherwise just take this one with you to your closest AC supply house and get a new one.  If nothing else, you will have eliminated this very common issue.  I've replaced mine even though they haven't failed but were showing some signs of puffiness.