There are three blend door actuators in the Caliber that control the flow of heat/AC to the various outlets. After you shut off the car the actuators will eventually reset to their default position. If the buzzing you're hearing is actually a failed actuator, perhaps it's causing some sort of weird electrical issue.
With the car running try changing the airflow outlets from dash to floor to defrost as well as turning on and off recirc. If you hear the buzzing then you have a bad actuator.
With the car running try changing the airflow outlets from dash to floor to defrost as well as turning on and off recirc. If you hear the buzzing then you have a bad actuator.