Posting for Krys2fur:
My wife'* car 96SE is having somewhat the same problem. It always only ran on low fan speed but, the heat worked. Then it stoped working and the repair shop replaced
the blower motor and relay. They called me and said the good news is that it is blowing hot air out but, the bad news is it'* stuck on high. He stated something about it would need to be reprogramed ??? And it would be around $800.00. I told him that would not be ok as long it was blowing hot air on high and then once it got warm we could just turn it off. He agreed that sounded like a good idea instead of paying out big money. Here is the problem now. It worked ok for a couple of weeks then, the display would go out and you couldn't shut it off. Even with the key turned off. It must timeout or something because, my wife told me this over the phone when she arived at work and we were concern that it would drain her battery by the end of the day. But she called me and started fine and the motor wasn't running when she got in the car. Now she says the heat is only working have the time. What could the mechanic be talking about?
Does is need a new control unit and if so, I'll hopefully find one at a junkyard. Someone told me usualy if it is stuck in high only the resister is bad. If that'* true where is it located. Any help would be greatly appreciated. Sorry I'm posting ontop of the original author but, I thought someone might be able to help us both in one post.

Krys.. check out this thread. I would think your blower control module may be acting up. Follow the test steps Randman listed and see if you have any luck.

http://www.bonnevilleclub.com/forum/...&highlight=bcm

Meanwhile, you shouldn't need to worry about blower draining the battery. It should shut off with the ignition.