From the symptoms you described it does not sound like it would be possible for a capacitor to cause this problem. The Capacitor, to put it in a basic way, gives the compressor or fan motor extra starting torque to get it moving by building up a charge. Most likely you will need to replace the time delay control (if that is not possible, you will most likely need a new circuit board).
Yes it sounds to me like a board or contactor on the board. If it is clicking to start or cycle it has power to do so. Most likely culprit is the board.
Awesome thanks for the Help now i just have to find a board or the relay itself and swap it. Thanks