In need of a little help concerning radiator fan assembly

So, I have a 2000 328ci. My radiator fan assembly is messed up. The fan stays on and will not shut off, so I have been plugging it in/out so it doesn't run down battery. I've been doing this for a while now...and now it is over-heating even with the fan plugged in. So my question is....I've researched and researched and I can get the fan for about $200....BUT my question is...could it be in the "plug" part where maybe a connector is broken? etc? Or maybe the "timer unit? Yes, I'm a girl, but I do change my own oil and brakes, etc(my brother taught me well). I just hate to spend $200 on the fan and the actual part I'm plugging into the fan sensor(or whatever its called) be messed up and I waste $200? To take it to the dealership they want to charge an arm and leg just to put on the rack and look at it....Any help would be apprecaited. You can send me a private message or email me at jms832000@yahoo.com I just need to get this fixed asap cause I was planning trip home in Sept and yeah...it's not gonna happen if I can't fix my car. Thank you all SO much. I've given up researching on my own, cause I can't find anywhere where you can just buy the plug to see if that is the issue first

Again, thanks so much!!!

"girl looking for answers in Louisiana"

i would probably start looking at a water pump or thermostat issue. if it's overheating there is a reason why the fan stays on so long

+ 1 on above plus Blocked radiator, defective fan clutch, wrong coolant used previously (too much phosphate screws up the rad even if it flows well). PM me if you want more in depth..