My air conditioner runs when the switch on the thermostat is in the off,heat,and air. The heat works like it is suppose to. The thermostat is a new digital hunter. I replaced the other digital thermostat because it was doing the same thing. Does anybody have any kind of advice or information about this problem?

With the little bit of info you gave us it sounds like the contactor may be stuck closed on the ac unit. Need moore info - Heat pump, gas heat or what. Is the indoor blower running also when the ac is?