i drive a 96 328is as well and had the same problem. What i did was found a guy off of ebay and for about $50 i sent the climate control in the mail, he fixed it, and sent it back.
Yea if i had of used the web site listed above it would of cost me much less, but this is assuming i could do it right without causing even more problems that wouldn't be repairable, so i would have to buy the part from bmw for about $400
If you think u can do it yourself, go for it, but if not id go with the ebay guy, just search "bmw digital climate control" and it should come right up
Mods: Tint, Euro Tails, Smoked corners and Side Markers, E46 Style Shadow Grill, 18" M3 Replicas, M3 Exhaust, Low Beam Silver Stars