Note on Fan Control Module --
About this time last year, I "lost" all A/C. I'd switch it on normally and everything would seem to work; the blower would come on at all four speeds as usual, the A/C "button" light illuminated, and the temp control worked; the only thing was that the temp would vary from warm-outside-air to heater-air -- NO cooling at all. What was not normal was that there was no "click" of the A/C compressor clutch engaging and no little blip in the idle as usual when the clutch engages. When I lifted the hood and looked, it was apparent that the clutch was not engaging and there was no evidence that the clutch was seeing any power in any condition of engine running, switch position, etc.
I went through everything. There was power where power should be and no power where there shouldn't be. The radiator fans worked normally in the "switch-on" test but they were both noisy (gosh, they were something like 10 years/250K miles old) so I switched them out - no difference, of course, but it gave me confidence that they were not likely to be part of the problem .
I rigged up a little jumper to the compressor clutch connection. With the engine idling and A/C switched on, there would only be hot air coming from the vents but when I attached the jumper at the battery, the compressor clutch would "Click" and in just a few seconds, there would be cold air at the vents.
At that point, I couldn't think of any issue that would be causing trouble except the Fan Control Module function. I had a friend move the A/C control switches from "off" to "on", change fan speeds, turn fan to "off" position, etc. -- there was never any power at the wire to the compressor clutch from the FCM under any circumstance. I decided to change out the FCM.
(Note: Dealer quoted "Genuine VW Replacement Part; $741.00"; our Trusted TDI Parts Online source offered "Asian 'pattern' part", $90.00; "OEM" supplier part "$189,00. Since I wanted this issue "FIXED - NOW", I went for the online OEM part although it was double the cost of the "pattern" part.)
The change out was simple and easy. There was no apparent problem with the old FCM (original to the car from new) - no overheating signs, no burned connectors, nothing; it just didn't seem to provide power to the A/C clutch. Once the new part was in, my A/C worked as usual and continues to do so since.
At no time during my A/C problems did any fuse blow nor was there any sign of malfunction or damage to any other part. Since your symptoms are very different from mine, I *suspect* that if your issue involves the FCM, you have a different problem than mine, but I wanted to let you know my experience with a bad FCM and how the problems and fixes presented at that time.