Ok. I have an 01 as well, 11/00 build, and I had the driver's door actuator replaced. It's not something I'd personally fool around with, I hate anything invloving removing door panels, I'd recommend you take it to the dealer for a proper diagnosis before moving on it.
I don't have the part #, but from time to time I see an actuator on ebay. In the meantime, try this:
http://www.realoem.com/bmw/partgrp.d...45&hg=41&fg=40
and this:
http://www.realoem.com/bmw/showparts...28&hg=41&fg=40