Hows' the battery gauge?
Leave it off and let it charge to 100%. then boot into recovery, and clear the following:
- Dalvik-cache
- Cache
- and Battery Stats.
and then restart the phone.
Maybe the battery is messing with it starting up, I've had a similar problem on my VERY OLD laptop about 5 years ago... (I know, that's a stretch, but I'm running out of ideas here!

)
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