NOTE: If the tablet is still under warranty, I would contact the manufacturer before doing anything further. Don't want to void any warranty. Now if it is already out of warranty, please look into the following.
It could be a few things. If you mean the screen shows that the battery is charging, then the display isn't dead (or it couldn't show anything), however, that doesn't mean that the battery itself isn't done for. Does it show the battery as fully charged?
You may need to do a "Factory Reset" or even a "Hard Reset" of the tablet to get it to work. The first will remove some personal data, the second removes all personal data.
To do a "Factory Reset" locate the pinhole on the device. Using something small, but not sharp (don't...