The heater control valve may be stuck open but it sounds like you have problems in the control head. With everything shut off there might be some residual airflow through the heater vents but not much.
This will be a vacuum hose loose or off in the engine compartment, probably on the passenger side of the engine. When you lose the vacuum supply to the A/C & Heater system, the default vent control goes to defrost & floor. HTH.
If the vacuum system seems to work and can move the flap axle of the heater control valve, the flap inside the control valve is broken into small pieces and disappeared. Take the valve off and see... Happened to me.
