I have a 2001 Audi A6 also, and I know just how crazy doing any electrical work in an Audi can be. If you let me know what kind of sound package the car has (Bose / non-Bose) and what kind of speakers and other equipment you have I will be happy to help you out if I can.
I have never installed a D3, but I have installed an AVIC-N3 and an AVIC-Z1 in my '01 A6 and installed an AVIC-N1 and N3, as well as an alarm, remote starter, and "carputer" in my '94 100S so I have a fair bit of experience w/ Audi wiring. Do you have the Bentley factory repair manual, either on a computer or hardcopy? It has tons of great info including complete wiring diagrams and schematics for your car. If you dont have a copy I can print out the pages you need as pdf's once you let me know the specifics about your car and sound system. To be sure I pull up the right info I need to know:
1) the engine type (2.8L, 2.7T, or 4.2)
2) body type (sedan or wagon), 3) type of factory stereo (Bose/non-Bose, Concert or Symphony series OEM equipment)
4) how you connected the D3 (via direct wire to speakers, speaker level input to stock Bose amp, RCA connection to Bose amp, etc)
5) any changes you have made (new speakers, amps, etc).
As for the cause of your problem, my guess is that you have the Bose system and either direct wired the speakers bypassing the Bose amp, or did not direct-wire them but didnt connect the amp turn on wire. You may also have amplified speakers (where the speakers are amplified by small amps directly attached to the speakers). These can cause all kinds of problems depending on what you have (they may not be 4 Ohm, may not be turning on, etc), but once you post more detailed info we can go from there.
Hope this helped at least a little, and hopefully I can get you the correct info so you can listen get your stereo working.
-Jarad