Blower stayes on after car is turned off

Blower stayed on after car is turned off. Also, air conditioner turns on and off when engine is on. Problem started with oe blower motor staying on after I pressed the off button and turned the vehicle off. I started off disconnecting the battery. Later I found out I could half crank the vehicle (just enough to turn over) and the blower would turn off. Well I changed the blower motor, put a brand new one on. Same issue. Well, after a tune up the blower would turn off with the vehicle, but I cannot get the air conditioner, or the blower motor rather, to stay on. It blows hard and cold then it cuts off. I tried wiggling cables and harnesses to no avail. Help me please