I am experiencing the same symptoms as described in the following:
My Nexus 7 is full discharged. I have it connected to Factory AC-to-USB adapter. It cycles through boot up, sounds a tone ... stays on perhaps for 10-20 seconds ... long enough to display "0% Charging" ... and then powers itself down, again with another tone. On some instances when it powers down the screen display shows 'static' with accompanying white noise sound, like an old television set.
I've had it plugged in for over 4 hours ... and its cycled probably 2-3 dozen times.