Overheating prob

[Azzam]

Hi,
i have a major problem with my 323ci e46 2000, it overheats when im in the traffic. The next day i looked at it in the garage opened the radiator cap (the car was cold) and i let it run for half an hour and examined the cooling water when the car was warm. The water was bubbling and boiling and the radiator fan failed to switch on.
So i went and bought a radiator fan but it seems it was not, it was a pusher fan instead! so it still fits and i have disconnected the radiator fan plug and connected it to the pusher fan and the pusher fan worked for a while when the car was warm.
I herd from a friend the water pump could have packed up. so i bought a brand new water pump and it did exactly the same thing!
I also checked on the tempreture meter said warm not hot or cold but why was the water boiling?

I also heard that the AC has to be fully charged to let the radiator fan working properly is this true?
and what triggers the fan to turn on?
please help me as it is hard to get to work without a car.