It ran great for a few months, then I recently I got some rough idle, which remided me of when my O2 sensor went out on my Firebird. It got rough and choppy, then would go back to running fine. A couple weeks ago I was out and it started to get hot, I came back to the house, it was running a little rough, but not bad. I parked it. Now when I try and start it, it starts easy, idles smooth, but then cuts out after a couple seconds. I can repeat this process endlessly it seems. If I try getting on the gas a little it just dies instantly and smoothly. If I give it lots of gas it will sputter a couple times and promptly die. I thought perhaps the fuel pump was dead, as I did not hear it pumping up. I removed the fitting(engine side)from the pump(external) to the engine and it was definately under pressure spraying in a fine mist as I slid it off till it could give a spurt when it first came off. I refitted it started the car, it died and then removed it again with the same effect.
Last part, when my brother brought it to my house, it was raining a huge amount and one of the roads was partially flooded so the bottom of the engine probably got wet. However I parked it and let it dry for several months before starting it up and as I said it ran very smooth idle, great pull, though I cant say I opened it up or anythign as I was driving it to see if I could find any issues with anything. I have replaced the radiator hoses and the one to the heater core, had gotten a couple cracks. I replaced some of the old relays, looked original, which made it a little nicer idle wise I guess, but it could have been me wanting to think I didnt waste money :P Hope you have some ideas of what I can do. thanks,
Tyrecies

 

When is the last time you changed out the fuel filter?

Your problem almost sounds more like a vacuum leak.
Is your oil cap on tight?
If so give a quick(but detailed)look around the vacuum hose layout, and check for any disconeccted hosed, or cracked rubber fittings.

It's a pain, but ensure you have no doubts about the system being in tact.

When you try to start the car again, have someone else turn the key, and then you can listen for the fuel pump to come on, and stay on..even after the car stalls.
If you have a fluke meter you can confirm good voltage to the pump connections to make sure it's not your relay.

 

The 1984 4000S Quattro came standard with Bosch Fuel Injection. Make sure all the connection lines are tight, NO leaks.