Have you tried a different charging cable?
Did you allow the battery to run down until it was completely drained?
- If so then try the following;
Watch this video (link below). You should only remove the back cover, disconnect and reconnect battery cable. Disregard the rest of the video as I could not find one doing ONLY what you would need to do. Follow the instructions to remove the back of the tablet then disconnect the battery cable(careful not to damage the circuit board), reconnect the battery cable, and replace the back cover. Connect the charger, within a minute the screen on the tablet will pulse/flicker which is good news, allow it to charge a while, turn on the device, turn off the wireless wifi, click the power button to turn the screen dark again, and allow to charge for another 6 hours or till fully charged (when not connected to wifi the background processes will affect the charge time, on a weak charger it may not even charge like from an usb port on a computer).
Again, you should only be concerned with the video up to about the 1 minute and 15 second mark. You only need to disconnect the cable then reattach it. ONLY DO SO if you are comfortable doing so. If you have never worked on electronics before or are uncomfortable find someone to do it for you.
Galaxy Tab 3 Battery Replacement and Screen Repair Disassemble and fix