Yes, the compressor never kicks on. While that's part of the problem for sure, it has to be more than that. Putting it on "vent" should not be blowing hot air in the dead of winter, and that shouldn't have anything to do with the compressor as far as I know.
Side note: DMCH has one door solenoid listed for purchase: SOLENOID DR LOCK LH. Am I correct in thinking that LH and RH should be identical and that's why only one is listed?