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Yea - that would be a good thing to do - assuming you have access to a simple compression tester gauge. TSI motors have a problem with failure of early chain tensioners (actually, there have been several VW revisions to that part).
I do have a tester, I'll give it a go.
If yours is an old original and has failed, it would certainly show up with a quick compression test. The motor would also sound "different" when spinning (attempting to start), if the valves are not working. Hope that's not your problem - it's costly to repair the bent valves and head work.
Honestly, before I realized that my car was doing the "smart-start" (does this have an actual technical and/or VW designated term??), I thought my car was actually started and idling at 300rpm. That's how normal it sounds. I gotta put some relays back in but I can get a sound/video clip of me trying to start it.
But I would think any problem with valve train timing would be flagged with an engine code - so doubt (hope!!) that's your problem.
Anyone in Metro ATL with VCDS that can swing by? Down to compensate ya with food, drinks, gas money, and good karma ;-)
It would help to verify basics - do you have fuel? Do you have spark?
I grounded the first spark plug (left side of engine as looking at it) to the engine and had a buddy crank. I saw spark in daytime (albeit a bit overcast) from 5 ft away. About a second or less in between, which makes sense at 250rpm /4 strokes = 62.5 full cycles per min /60 sec = 1.04 cycles/sec. 1/1.04 = .96 seconds for every plug fire.
I pulled the soft feed line off the HPFP and it seems to flow out plenty. Havent tested past the HPFP besides what OBD11 tells me.