| The main power connector wiggling loose is common. And all you have to do is jack up and safely support the car, feel around for the plug, then push it back in.
The fan is a piece of cake to change - two nuts and a quick fit connector, but the fans aren't cheap. But normally if that's the problem it will blow the fan fuse which kills the fan on the radiator too. (My car had this, and I reported it as an electrical problem killing the fans. Adelaide Motors - aka Adelaide MINI Garage) charged a *&%&%* fortune to pressure test the cooling system cause it was overheating.)
Finally, there is a thread of mine regarding the connector on the back of the alternator, but that doesn't sound like your problem.
Good luck!
R56 MINI Cooper S JCW Challenge | 
