My Android Precedent shows fully charged but will not power on. When I hold the power button for 10 seconds I get the green battery icon for about a second and then it shuts off.
If you can get to it, select Wipe Cache Partition instead of Wipe Data/Factory Reset, since the latter will wipe your phone, while the former does not erase personal data.
If that doesn't help, consider trying a new battery. I know the icon shows a fully charged battery, but try it anyway.