Have you tried leaving your Galaxy tab 3 on charge overnight, I would advise to try this first? Does the LED light appear at the top of the screen whilst charging? If so, then you could try a soft reset. To do this, press and hold the Power button, the Home button and the Volume up button together for 10 seconds until the Android logo appears. This will prompt you to reset.
If the LED light does not appear, please check out this link to service your Tab 3 http://www.samsung.com/uk/support/supportcentres/.
Hope this helps.
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