I have been through all of the posts and have seen somewhat simular ones but none that quite match up.
I have an 01 Allroad with the 2.7t TT. A week after I bought the car I found out it had a bad o2 sensor and the valve cover gaskets were leaking very bad. I replaced the gaskets and bought all 4 o2 sensors but wasn't in a hurry to replace those since I had been told they would not affect it too much overall. I also bought the crankshaft position sensor but have not installed that yet either. I have gotten 2 codes, the first for o2 says bank 1 sensor 1 no activity and the other just bank 2 sensor 1. The car started out with the 15 min delay before restart after driving even for short distances and now takes around 4 hours. It will not restart untill the engine is stone cold. Only once, it sputtered like it was out of fuel and died while driving. I replaced the feul pump, fuel pump relay, Coolant temp sensor. It is still doing the same thing (crank with no restart). After the ECT change it tried a little harder to start but still would not untill cold again. PLEASE HELP!!! Im tired of throwing parts at this thing without knowing whats wrong! I just want it to start everytime so I can trade it off. Thank you!

 

Try resetting ecu. Take out ECU after disconnecting battery. Let sit five minutes and reintall. Buddies A6 had same problem and it was something in the cluster with security system shutting off the car.

 

Hey, so even though it was a different car, I had a similar problem with my 00' a6 4.2. What would happen is the car would start fine cold, run for 15 to 20 min until hot and then just die on me. Wouldn't restart until until it was cold. The problem turned out to be the heat shield covering the crankshaft position sensor had been bent somehow so the sensor would over heat and stop working. With a new heat shield and sensor, car was running like a champ again. Only difference was I would sometimes get a code, but not all the time. You said you already had the part, so i would look into that as it might be the source of your problem. Not sure if the O2 sensors could play a role, because It seems like any problem not matter how small can cause a plethora pf problems in these cars.

Anyways, hope that helps and good luck!