Hey Rufrob - From your description of what is happening after your car starts - it sounds like you have all the basics (Gas-Air-Spark). This means your computers are both up and running. Perhaps your engine is stalling out from being over fueled. There is a water Temp II sensor that can cause starting and running issues. The S4 928 Temp II sensor works a little different than our S2 set up but have the same function during the warm up cycle.
To test the Temp Sensor II there are two separate temperature sensors housed in the one sensor body. Prong 1 is the sensor for the Electronic Ignition and prong 2 is the sensor for the LH fuel injection. The resistance reading from each prong to the sensor case should be in the range of -
0 C / 32 F: 4.4 to 6.0k Ohm
15 - 30 C / 59 - 86 F: 1.4 to 3.6k Ohm
40 C / 104 F: 0.9 to 1.3k Ohm
60 C / 140 F: 480 to 720 Ohm
80 C / 176 F: 250 to 390 Ohm.
You still can drive the car if the temp II sensor is defective - just disconnect the sensor. The S4 model brains notice that the connector is off and use a pre-programmed warm-up time to adjust the mixture upon start-up. Starting might be a bit harder but once warmed up, the mixture will be correct.
Good Luck, Michael