<i>if the blower works only on low, it is worth checking the resistor, I would imagine this could be your issue. Check this tech article:
http://www.pelicanparts.com/BMW/techarticles/BMW-3-Series-E90/ELEC-Blower_Motor_and_Final_Stage_Replacing/ELEC-Blower_Motor_and_Final_Stage_Replacing.htm
-Nick at Pelican Parts </i>