Does the tablet stay on when you unplug it? If it doesn't then most likely the battery is bad. You should also look in the charging port and see if any of the pins are bent. It is possible that the cord or the brick you have is bad as well.
If the tablet does stay on when you unplug it I would try to wipe it back to factory settings and see if that does the trick for you. Make sure you back up your data before you wipe it though. There's no way of getting back after you click the button!
Best of luck and post if you need anymore help!