cliamte control problem...help!!

im posting this in here because the i beleiev the climate controls are the same from the suburban/tahoe/yukon family. its an 06 denali

ok, just noticed this problem today when my girl frined was complaining that the heat wasn't blowing. I just told her to wait till the truck warms up, then the fan will come on. Well, plenty of time went by and the fan never came on. So just as im about to start pulling fuses, the fan comes on...full blast. Ahhh, great.....wait, not so fast...i can't turn the fan down, when i lower the fan speed on the LCD screen all the way down, it shuts off again. So...i can't get anyting but full blast or off. I can't even get it to go full blast when i want it to...it just randomly goes on for a while then shuts off. You can hear it makes several attempts to go on for a second before cutting off sometimes. One more strange thing....i turned the car off with the fan on full blast, and the fan stayed on, no key inthe ignition. Ummmm ok....this is deffinatly not what i need to be dealing with for a 60 thousand dollar truck.