First of all, thank you for the all the reply's. I appreciate it.
I live in Coventry but I started searching for a specialist in Birmingham, maybe I find more options. Big garages want me to leave the car for 3-4 days but I cannot do that since I go to work every day. Even Kwik fit wants it for 2 days because they don't have the specialist there all day.
If you know any specialist that can take a look please let me know. I can even go further that Birmingham this saturday, and wait for a few hours there to fix it, is not a problem.
I assume the fan is the one in front of the radiator and yes, it doesn't work. I identified the relay, tested it and it works fine.
I pressed the demist button and the compressor or the ventilator still don't start. It just takes the Climatic sistem's fan to maximum and switches the flow of the air to the windscreen.
Posted two photos, one with the interface of the climatic system and one with the ventilator that I assume we are talking about (I can see it thru the bumper grill, the photo is from google)
