Of course now that the heat finally came I noticed the air con is not working. The aircon service guy found out that a valve was leaking (the larger priming one next to the radiator) and we managed to fix it so he checked the airtightness of the system and charged the Freon, but the aircon is still not working. He noticed that the electric fan is not starting. When I press the A/C switch there is a change in the way the compressor works, also the temperature seems to be a little colder than without AC but just for a few minutes. With temp controls all the way down, the air is not ice cold as it should be. The pipe coming from the radiator is hot as the aircon service guy says it should be, but he also says that if the electrical fan is not spinning, the compressor is decoupling at a certain temperature level. Could the computer sense that the fan is not working and then disengage the compressor?
We tried to power the fan separately but it’s not turning. From the looks of it the fan motor seems expensive. A friend of mine with a similar Range but from 2003 told me that his fan is broke for a year now but the air conditioning is working even without the fan. He didn’t replace it because of the price. Before I invest in a new fan, can I know for sure that the aircon will start if the fan is OK? Is the electric fan contributing to the engine cooling too?
This morning I measured the electrical fan’s connector and it is providing 12v all the time. This means that by separately providing tension to the fan, it shouldn't necessary spin, right? How can I find out if it's working? Thank you!

A small update, I went to an electrician, he powered the fan just like I did and showed me the sparks and said that the fan is shorted and that I shouldn't have 12v on the connector all the time. He said that normally there is a thermal relay that provides tension to the connector and he suspects this relay locked and the fan spinned all the time until its death... Is he right?

Also he said that normally I should get some cold air at start until the freon circuit overheats and either the A/C compressor disengages or the pipes blow... Will check the cold air at start later as of course today it is cloudy and my tests with A/C on/off become irrelevant...