Weird fan problem

The AC/heater fan on my 2000 3.1 Buick Century seems possessed. The #4 setting on the fan went out a couple of years ago, and sometimes #3 will quit also, but 1,2 & 5 seem to still work, so wasn't a big deal. Now a few times, the car will be parked in the garage with the keys out and the fan will start on it's own. First time it did it - had to pull the battery cable to get it to stop - the switch wouldn't shut it off. Next time it did it - switching the fan settings up and then off turned it off. I don't know if it does this other times when I'm at work and can't hear it and it stops on its own - or if I've just been lucky and it has only done it at home or if I'm going to have a dead battery one of these days.
I need to know do I replace the whole unit that has the AC/heater switches - is it in the switch - relay?

Thanks

Replace the fan resistor as it is probably bad and causing your problem. Especially since certain speeds do not work. You my want to purchase one from a dealer and they are different from automatic vs. manual climate control.