I had a similar issue with my Nexus 7, and sent it in for repairs against their Global Warranty. The local agent for repairs is Partserve, and boy did they give me hell. I only got my tablet back in full working condition 7 months later and after lots of fighting with them.
My tablet would only charge if it was switched off. If it was still on, plugging the charger into the Micro USB port would do nothing. I recall having to do something to get it to at least charge while off. Google around, and you might find something. I believe its a known issue with this tablet. I think you have to put the power cable in, and then boot into the bootloader (power button + volume down?), and change a setting. Then it will charge while the tablet is off, which is better than not charging at all.