I opened the compartment to the outside unit and there were three things. A circuit board, something that looks like a small canister and a switch that looks like a relay. The circuit board has a flashing green light. When it is switched to cool there is a click followed by another click. But nothing happened. Ok what do I need to replace at this point. This unit is zoned cooling. Sorry I did not mentioned the zone cooling the last time. Nothing looks swollen or burnt.

You first need to insure that you have power ( the flashing light gets it power from the furnace) Check breaker, check fuses in disconnect box on wall near A/C, look at canister (capacitor) and see if the top is ballooned , indicating that it is bad. Good luck

Be sure you have power to relay(contactor), the canister is probably a capacitor.
Could be fuses or breakers, 1 location is outside, the other probably in main panel.
That is if board is 24 volt powered. If 240 volt, your breakers probably good.
Power goes into Relay, and when it receives 24 volts ac, pulls in, and makes contact with load,(The compressor, and Fan)Both probably didn't go bad at same time(Could).
With insulated tool, you could momentarily press in to test, If Compressor and Fan come on, it is A)open coil on contactor or bad contacts, Control wiring, thermostat, transformer, fuse.