I've got a 2003 A6 Quattro with a blower that quit blowin'. I understand after checking the fuse that it could be either the Blower or the Blower controller ( resistor ) that has malfunctioned. But nowhere have I been able to find out out how you test for which ? It dosen't appear that there is an appropriate error code for the diagnostics. Does anyone have a way to test short of removing both ?

 

I think you'll have to remove the motor to test it. IIRC it's not too terribly difficult after getting the glove box out. But I could be thinking of a different car.

 

I have a 1998 but should be close enough to get you started. I put some pictures on my profile. Try turning the control unit to fan only, then up to high to see if the blower runs.
You can drop the glove box and take a look at the blower control module. If there is a burnt connector is it probably that. To be safe you can remove the blower motor and connect it to the battery or maybe attach wire to 12 volt battery then touch the wire to the blower motor (maybe dont have to remove it) and see if it runs.