I've had a Nexus 7 for a couple of months now and recently had an issue where the device would not power on normally or charge. I understand that this may be a precautionary measure from draining the battery fully.
I began searching and found the following procedure whereby you can recover from this issue.
- Plug the Nexus 7 into the wall charger.
- Press the Volume Down and Power buttons at the same time.
- When the Bootloader menu appears, use Volume Down until "Power Off Device" appears.
- Press the Power button.
- When the Nexus 7 powers down, unplug the charger and then plug it back into the wall charger.
This worked for me, but there is another recovery method that you can try here: