My A/C won't turn off the set temp is at 78 degrees but it keeps cooling past that temperature its 67 degreres now according to the thermostat. When I take the cover to the thermostate off then the A/C turns off. When I put the cover back on it starts up again and won't turn off. Is my thermostat broken. Or what else could it be

Yep, sure sounds like the thermostat is shot. Replace it and you should be good to go. If you can let me know what colored wires are hooked to which terminals in the old stat, I could try to help you wire up the new one. If you would let me know how many wires there are and what colors they are, I may even be able to suggest a good stat for your heating/cooling system.

Please also let me know if you have gas forced air with a/c, or a heat pump.