Might have better luck in the techincal section or MK6 section as it is a very specific question.
But, I throw one idea out there.... this happened to me on the MK4, but I'm unsure if that translates to the MK6.... I forgot to plug in the immobilizer plug on the steering column (tiny single wire that works with the key) so the engine did nothing. If you changed the steering wheel to something non-stock, this could be the answer.
Just one thing to elimnate from the list.
Regarding oil pressure question... I have nothing to offer in this area.
Best of luck. Nice to see newer generation cars on the track.