You might want to see if the battery connector is actually completely connected. You would have to, "very carefully" take the back of the Tablet and see if the battery connector is fully attached. If it is partially off "very gently" press it back in and this should resolve the problem.
If this doesn't do it, then you would have to try a "Hard Reset" of the device.
NOTE: Doing this will clear the data on your tablet, so it is suggested you not choose this option unless you have to, or aren't worried about losing anything on the tablet.
To "Hard Reset" the tablet...
1. Make sure that the Samsung tablet is actually powered off.
2. Press the "Power" and the "Volume Up" buttons, together, until you see the start-up logo on the screen.
3. Once you can see the logo, release the buttons and allow the device to enter the Android system recovery mode.
4. Next use "Volume Down" button to get to the "wipe data/factory reset" option When in recovery mode the "Volume Up" and "Volume Down" buttons are how to can navigate and highlight what option you need.
5. Once you have selected the "wipe data/factory reset", press the "Power" button to select that option.
6. On the following screen, repeatedly press the "Volume Down" button until the "Yes - delete all user data" option is what is selected.
7. Then press the "Power" button to hard reset the tablet.
It should restart itself and be working after this.