In that case your situation sounds like what happened to my first N9. It wouldn't start up as far as the vibrate signal, but it could be flashed, erased, MALF state cleared, rescue kernel loaded and flash partitions mounted, etc. I suspected screen and prox sensor as you did, but replacing them didn't help. I never did try a different battery, and ended up replacing it. A trip to a repair shop in the UK (no N9 support in US) got me nothing but a refunded service.fee and out of pocket a little for my half of the shippi.g.

My suspicion in my case is a hardware problem, and I'd suspect it in yours too. Since the phone never restarted after going from warm indoors to well below freezing outdoors for a couple hours to clear snow one brisk March day, thermal shock is my prime suspect. Speculation, but a marginal solder joint could easily use thermal shock as an excuse to go hi-Z for good. Maybe even that proximity sensor header. But I've never gotten around to looking up the specs I'd need to give a little hot air smd rework attention to the likely suspects.

Good luck with yours. Make sure to post if you find the culprit.