Car Died Right After Start, Cranks Now But Won't Start
 

Went to start my car last night real late and it turned over, fired for a brief second, then died. It cranks now, I can see the belts turning, but it won't fire. What do I need to check? Should the fuel pump be loud enough to hear it priming when I key on? Any help would be much appreciated...

Couple things to check....
 

BDTD a couple months ago, it was the fuel pump.

(I have a 2001 C5 A6 2.7T APB, so these facts might differ from what you have..)

You shouldn't hear the pump priming when only the key is on, it only runs when the engine is cranking. (Via the '372' relay) If I recall correctly, the 372 relay will only engage and send 12v to your fuel pump if it's getting a good signal from your CPS. Pull your back seat cushion and the access panel on the passenger side to the top of the fuel pump, check for ~12v when cranking on the Green/yellow wire. (I have such an access panel on my A6, not sure about the S4...)

If you are getting good cranking voltage at that wire, then you can rule out the CPS, and 372 relay. (At least from what I understand...) I ordered my new fuel pump from EuropaParts, a VDO brand, dropped right in and fired right up. The only hassle was draining out ~18 gallons of gas, I had just filled up before the pump failed!