You could have a couple different issues but it would help to be clearer in your explanation.
You say there's no air flow - do you hear the fan motor running? If no, then the problem could be the switch, the harness to it (burns up at the connector), fan motor, or resistor. If yes, then the problem could be the actuator on the driver end of the box as east302 pictured, or worse, broken doors in the distribution area of the box, that the actuator operates.
The temperature actuator is the one you're hearing, and it's in the middle of the box. It won't be responsible for anything to do preventing airflow; it does operate a door that divides the heater core and evaporator core, affecting the temperature of the air blowing through the system - but the air will blow regardless of what that actuator does, it can only affect the temperature. It's normal for it to make some noise while it operates. If it runs continuously then it's bad or the controls are bad.
Richard