Have you tried a different battery? It could also be that it will not hold a charge to power it on. When it is plugged into the charger, will it turn on?
A properly working phone is very important, so lets bring this battery back to life! I see that you have already completed some great troubleshooting so far. Were you able to try a different charger? Has there been any liquid or physical damage to the device? If the device shows a full charge and the device will not boot, it could be the software not working properly. If the software has become corrupted, then a Hard Reset would be the next step. I have listed the steps for a Alternate Hard Reset here, please start at step #3 http://vz.to/tC9oiG . Keep me posted.
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This is similar to what's happening with my phone! It will just shut off by itself then when I go to turn it back on the battery indicator shows up showing a drained battery (even though it is in the 90% range!) and will only turn on after plugging into a power source. This issue just started on our way out of town (especially frustrating as I left our GPS unit at home because the one on the phone worked better).