Halderman: From your description, I think the blend door motor is no longer working. The door is stuck in one position. The control head could be the problem as well, causing the door not being commanded to move. If it is an auto climate control, hooking up a scan tool should show some codes or data on the HVAC system.
The air conditioning compressor typically runs all the time anyway if it is auto climate. When it is very cold outside, a sensor will keep the compressor from running until the engine gets to a certain temperature. If the air does not come out the right vents, then my guess would be a control head problem.