Seems like your climate control finally gave up, meaning the resistor is probably fried and that's what causing your unit to stay dark or come back on unexpectadly. You can fix it yourself if you have time and patience. You will need to remove the climate control, take it apart, get the replacement resistor, which is about 0.49c at Fry's or such electronics place. You can also have it fixed for about $50 if you don't want to deal with all that. I did it myself, took me about 1 1/2 to get the unit out, take it apart, remove the faulty resistor, sother the new one, put it all back together and put it back in the car.
I did all that following the instruction's fron this guy's website, who to me is a genius for taking his time and putting it all together.
go to the link, and rest is up to you. If you want to fix it yourself, follow the instructions.
If you want someone else to do it, there is a guy on eBay in New York, that can do it for you. In search field on eBay, type in E36 climate control
Hope that helps.
LINK:
http://www.macadamizer.com/bmwfix.html 
Linear Mode
