I assume you have the crazy wireless remote?
My Compressor usually doesn't start for a few minutes after the fan starts, which is normal-especially if I just changed modes on the system.
I honestly can tell you that the troubleshooting is not too bad if you're capable of using a good multi-meter, if not I wouldn't mess with any of this and plan on replacing the unit. You can still buy Carrier ACs that were overstock units and are perfectly good to go.
Remember- to truly reset the AC you must shut off AC power and pull the 12V fuse-I think it's for at least 30sec?