You can check if the clima compressor is working in a easy way:
Go to hidden kombi menu. Monitorize fuel consumption (L/h) menu 04.01.
Check the fuel consumption with the snowflake button on and off (set the temp to the low value first)
If there is a noticeable change on the consumption (from 0.7 to 1.3l /h approx) your compressor will be apparently ok and the gas too.
If the value doesn't change at all, your compressor is not engaging properly. It could be for many reasons, but you should diagnose the car and check the IHK and JBBF codes.