Hi,
If it's a Klima system with a dual-display, it should definitely have a fault memory and a self-diagnostic function.
The climate control actuators are a recurring problem across all Audi model lines. The issue is that carbon dust, which forms on the commutator due to wear, eventually causes short circuits. This prevents the current from flowing through the motor windings, instead diverting it through the commutator itself. A solution can be either a completely new servo motor or disassembly, cleaning, and possibly replacement of the carbon brushes (which are compatible with those used in Märklin model train locomotives).
You can find the instructions on how to switch the climate control system into diagnostic mode, as well as the meaning of each channel, at
http://www.meckisforum.de. If I remember correctly, it should also be possible to control the individual motors directly.
Best regards from Berlin.
Olli.