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I have a 94 C4 with the automatic climate control system. My original issue was with the controls and after replacing the Programmer module and cleaning the contacts on the indash control all was working as designed. I drove the car home from work on a Friday and let it sit for 2 weeks and when started up the AC was not working. All of the controls seem fine but the AC clutch is not engaging. I have checked/replaced the AC clutch fuse but no luck.
Are you getting a flashing light on your system? If you are you might want to run diagnostics and let the unit tell you what is wrongs. I bet you have a "09" meaning low freon.
I think I'd jumper or replace the clutch cutout relay before I went after a clutch or compressor.
With the ignition switch in run there should be 12v on pin A of the socket. If that's there jumper the relay and see if the clutch engages.
Don't need the car running for this test.