I would check for power and proper ground to the fan once the system is operating. Also, make sure the compressor is kicking in when you activate the A/C. The simplist thing to do first is check the fuses. The owner's manual will tell you exactly where it is. (in glovebox, undo two camloc fasteners, and pull panel down) If the fuses are good, I would suspect either a compressor fault, or a cooling fan fault. Checking for power and ground at the cooling fan will tell you if it is a fan motor or not (with the system operating)
If the compressor doesn't kick in, then I would suspect a pressure switch. This can also cause your fan issues, but if a pressure switch is not satisfied with the pressure in the system during operation, it will shut everything down.
I'm ASE Certified in Air Conditioning, and my primary experience is with domestic vehicles, but it all works off the same principle. I also have the 1500-page factory 3-series Bently service manual for '99-'05. I am responding to your cooling fan ailment after looking at the wiring diagram.
Let's just hope it's not the IHKA Control Module. Those can't be cheap, and they run the entire HVAC system.
Let me know what you find.
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