Nexus 7 Not Booting; Backlight Turns on while Charging
My Nexus ran the battery flat and would not restart, although I did not have the backlight issue that you mention.

There are a number of tricks suggested at:
https://support.google.com/googleplay/answer/2668668?hl=en
which involve powering on and pressing volume buttons.  This worked for me and the Nexus now behaves as well as it ever did.