Radiator Fan

I have a Jeep Cherokee 2000, 108,000 miles and the engine is V6.

The other day, I tried to start my car, but the battery for some reason was drained.

I installed a new battery in the car, then I noticed that the radiator fan would not turn off even after I turn off my car. So in order for me to turn the fan off, I had to unplug my battery so that it would finally turn off. This morning, I plugged the battery back and the fan didn't turn on ( good I thought. I thought my problem was fixed) but now even when I turn my car on or turn my air conditioner on the fan does not go on at all? What can be the problem?