Stumbled across this the other day – When your Nexus 7 Runs out of battery and has to shut down, it get itself into a state where it wont power back on, mine even went through a constant reboot phaze. To fix this:
1) Plug in the charger and press the Power button and the Volume Down button together.
2) You will see a menu pop up. Use the Volume button to go down to Power Off and press the Power button to select it.
3) When the Nexus 7 turns off, remove the charger from the device and then plug it back in again.
4) You should see the battery sign appear if it worked.