I suggest putting a scanner on the car, getting as much realtime data as you can for those 2 minutes, and comparing with someone else's stock running 4.4 to see if you can find where your fault is. If the wiring is suspect, you may not get a check engine light even if it is out of parameters, though you would think that if it refused to run, the ECU would throw a code as to why it believed it was not running.

Good luck, that does not sound like an easy diagnosis to make but it looks like the dealer is at least helping by not sticking you with the costs of the things that don't fix it. I don't know anyone that isn't a dealer that has tuning software for these cars.

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2001 E53 3.0 5pd