I have changed the coil because it looks like it had a spark or got hot because there was black soot on the power terminals so I replaced it but it still doesn't work. When you turn it on there is a small hum the magnets are not being pulled in, when you push them in humming gets louder from the coil and it makes a few clicks and that's all. The fan can spin if you move it but it won't start. What are the symptoms of the compressor being shot or is there something else. Any help would be greatly appreciated.

Did you replace the contactor or just the coil? (the coil is in the contactor) when you push the contacts in does anything run? Is there line voltage to the outdoor unit ? (tripped breaker)

I changed the whole unit when you push in the contacts nothing happens makes a humming sound and makes a few clicks the breaker is not tripped either.

Turn off the power and check the wiring on the compressor, they have been known to burn off the ends of the wires due to loose or rusty connections, next look at the capacitor (a round or oval canister with two or three terminels on top) is the top ballooned and not flat , this would mean it is bad. Some times it does not show a ballooned top to be bad , you need to check with a capacitor analyzer to be sure.It kind of sounds like this might be a good possibility.