Cranks but won't start on 2000 Audi TT Quattro

I'd been having an intermittent problem with my car deciding to suddenly not restart after short drives. And a couple weeks ago it quit starting all together. The mechanic had it for a week, but only ever replaced one fuse for the computer, and then couldn't duplicate the problem. There are no codes coming back, but at one point in time the mechanic got an error that the air bag wasn't communicating with the computer, but even that error went away. I can hear the fuel pump kicking on, i've got compression and fire as well. I've replaced the battery, and the positive battery cable (which was in dire straits), the starter is fine...My auto knowledge is limited and i've simply ran out of ideas, I hate to take it back to the mechanic because they can't find the problem either. I also noticed that when the car suddenly decides it doesn't want to start, the radio will magically come on even with the key out, and if you turn the key on, the defrost/ac/fan will give a yellow flashing light and will become inoperative. Anyone have any ideas on something specific, or does it sound like a short, i'm not used to audis, and I am flat out stumped

Asked by for the 2000 Audi TT Quattro
I made the original post, just wasn't signed up yet. The car has gone to a different mechanic, since the first wasn't finding any problems... 2nd mechanic made the discovery that the primary fuel pump has gone out, and was on its way out for the past month, but would sometimes function properly, hence the intermittent problem. I was already aware that I had two fuel pumps, but am not familiar with the use of "primary" versus "secondary", have only heard of them referred to as internal and external. Does anyone know which one is in the gas tank. Trying to find the part cheaper than the $450 that the dealer wants to charge me, but not entirely certain which part i even need to be looking for
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Hello, I had a similar problem on my 2000 A8L.
When cold the car ran fine. When a little warm it wouldnt.
So there is a sensor that cost me like under $10.00 from dealer.
It controls the temp gauge and sends info back to the throttle body.
It comes out after you pull a clip, unplug. It is cheap and most likely
the issue
what was the part