would my A/C power button affect the A/C compressor from kicking on?

Hello! It could be either. There could be an issue with power before the switch circuit or after, or something with the compressor itself. You'll want to have a shop diagnose it. Trying calling around to shops in your area for a better idea of possibilities and pricing. http://repairpal.com/mercury-repair-in-louisville-kentucky-40299