Apparently if you disconnect and reconnect the battery, then plug the unit back into its factory wall charger, you'll convince the tablet to wake up and try charging the battery again.

The only bad news about this is that it's not as simple as removing the back of a Galaxy phone. In fact, it's possible that attempting this will void your warranty, so proceed with caution!

Getting the back off requites gently prying the edges away from the screen in the little crack between the screen and the case all around the perimeter of the screen. Doing this properly requires a thin plastic pry tool and some patience.  Do not use a knife as the metal can scratch the case or even potentially cause a short inside the unit. We have readers write in to say guitar picks and old credit cards also can be used. By all means, be careful and DON'T FORCE IT! Work the pry tool around the edges until the screen separates from the back casing by itself without any force.