Air condition still runs AFTER ignition is turned off

What is your question?

Air conditioner set on 60 with the lowest fan setting (blowing on face) While driving the fan blew at high all by itself, yet the control panel shows it still on the lowest setting. If I TURN OFF the Air conditioner it still blows but on the FOOT setting. When car it TURNED OFF the air conditioner still runs and WILL NOT shut off. I have to disconnect the battery to get it to go off. Once I turn the ignition on again the air starts up in the OFF mode in the foot setting. What is going on?