My wife's 2003 A4 1.8t has had a starting issue for well over a year now and several repair shops have been unable to diagnose it. Basically, the car would intermittently have an issue where the engine would turn over but immediately after the initial "rev" it would die. Sometimes it would take 5-10 attempts to get it started up. I've seen several threads on this topic with various potential fixed but none seem to worked (or the other symptoms weren't being exhibited by her car. Anyway - after changing the spark plugs and noticing some oil around them, I determined the engine needed a new valve cover gasket. In the process of replacing it, I found that one of the rubber elbows connecting one of the PCV lines (official name: Elbow Hose Air Pump Pipe to Check Valve Pipe) that needed to be disconnected to replace the gasket had completely cracked. The crack was hairline around one of the raised edges of the elbow, so during any routine visual inspections, it wouldn't have been noticed. The connection appeared intact until I went to disconnect the line and found it was completely separated. The elbow in question is shown in the below two pictures, but it would also be worth inspecting the other elbow for the other PCV line next to it (this appeared to be rather new compared with the cracked one so I have a feeling it was replaced at some point. I didn't have time search the car's records though). This elbow is part # 058133785B with a retail price of ~$30 at the dealer (mine had one in stock and I didn't want to wait for shipping). It can be found online for less than $20 from a variety of sites. I would also recommending picking up some hose clamps as these use the "one time" clamps that are virtually impossible to re-use.

Hope this helps a few people out!

Location on engine:


Close-up of the new part installed: