Recently I was using Nexus 7 and the battery got to the point where it powered its self down, so I put it away...This was the issue I forgot to put it on charge once I got home, a few days later went to put it on charge and it kept cycling to the Nexus logo, the google logo, turn on bleep and then off again, nothing was working. I spent hours searching the web and finally found a fix hidden away in a forum.
The fix, is really east once it starts to turn its self hold in all 3 external buttons in together, you will have a menu come up, using the external buttons again cycle through until you come to "power off" hit the powere button to confirm the action.
Disconnect the power cable, re-connect and boom! The device should be charging!