Here are instructions to replace the dreaded AC control panel. In the early E38's (95'), the display pixels commonly go bust, and cannot be repaired. The only option is to replace the entire control panel unit, and it's not cheap. The best option is to find a unit from a newer car, which has a somewhat different design, but is a direct replacement.
I found one used, and although it's cheaper than new it's still costly. The replacement is easy though:
With a screw driver, or preferably another flat instrument that won't scratch, pop out the upper part of the panel carefully. About half inch from the edge on each side works best, because that's where the clips are. It should slide out pretty easily.
Side by side, the "old style" and the new style units are have connectors in different places, but they are all the same. No modifications are needed to install the new style unit.
Plug in all the connectors and slide the unit in until it snaps in place. The entire operation should take no more than 3 minutes.