I wanted to create this thread to hopefully help others. I have been dealing with a very frustrating hard or no start issue, which only occurs after about 30 min to a few hours after driving the car. Never had issues with cold starts in am or right after starting the car up. Car drove great otherwise. Unfortunately no codes to help guide me and battery tested ok. All I could notice is that if the car was not turning over, I could push the throttle while it was cranking and the car would start up.

I'll save you the details about why other things like fuel pump did not make sense. I was going over the engine study guide and thankfully something stood out. The evap purge valve allows fuel vapors to be drawn into the intake and connects at the top of the charge cooler assembly. Unfortunately the evap (N80) valve would also hopefully throw a code if malfunctioning. However, there is a small one-way valve between the N80 valve and where the hose connects to the charge cooler assembly. It lies right under where the aluminum turbo intake pipes connect to the plastic intake assembly, or Roc Euro etc. if aftermarket. If this valve fails, then it allows fuel vapors to travel into the charge cooler. If the engine is off then enough time will pass so that fuel vapors collect in the charge cooler. When you go to start the car, the engine will draw in the fuel-rich air from the charge cooler and intake manifold, then will add of course more fuel via injectors, thus creating a rich AFR that will affect the ability of the car to start. It makes sense that the engine will start when pressing on/opening the throttle because it would allow fresh air in the intake, thus leaning the AFR back out. I hypothesize that when enough time passes (like overnight), the fuel vapors have enough time to dissipate outside of the intake tract and so there is no or minimal effect on the AFR of the intake air.

Of note, it might also cause the car to idle higher as well (due to rich condition in intake air), but I have not seen this in my car.

I decided to test my evap theory by unplugging the hose to the top of the charge cooler assembly after driving home today. An hour later I plugged the hose back in and started the car. It started right up. Well holy shit. Now, it does not prove that the valve is the cause of the issue, but at the very least the evap system is the culprit.

I then decided to look up the valve and unfortunately the valve does not have a VW part number on it and the evap schematics for the 4.0T (on places like audiusaparts) does not contain this info. Called up the local stealership and they were not helpful either. After literally an hour googling, I was able to find the part number. Here you go:

058905291B - This part can go fuck itself btw and audi needs to update their schematics. Sorry, I am just mad that I wasted so much time finding this thing.

Now, I have yet to change this valve out but should have it in later this week. If my issue returns, then I will probably look further into replacing the N80 valve too.

Hope this helps.