Audi A6 Avant 1999 stumped mechanic

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Our mechanic has given up. About 10% of the time we attempt to start our Audi, it doesn’t turn over. It tries and sounds normal but doesn’t actually catch. If we wait anywhere from 5 min to recently we even had to wait an hour, it will start upon additional attempts as if there was no problem whatsoever. Occasionally it sounds like it might stutter and shut off again after it has started, but generally not. Battery is new. Starter checked. Alternator is fine. Put in new Engine Coolant Temperature Sensor. Our mechanic has begged us not to bring it back because he is finding it extremely frustrating that he can’t figure it out. Any suggestions? It has about 105,000 miles on it.

Fuel pump. You try and wait the fuel pressure builds each try and then it has enough to start.

“turn over” means that the starter is turning the crankshaft of the engine. The correct thing for you to say would be "it turns over, but the engine doesn’t start."
These questions are easier to answer if you use the correct terms.

I think there are at least two possibilities here.

  1. Failing fuel pump.
  2. Leaking fuel injector.

I think that it’s more likely to be #1, because normally it would run badly for a few seconds after starting if it were #2.