Most causes of this is a hardware failure, usually on the system memory. Try booting to the recovery options and do a factory reset. If that does not work, next thing to try is to flash the stock ROM on it using a computer. Do a search for your device and stock ROM, for the Tab 3 I'm sure there are several downloaded somewhere.
You can also try removing the battery and holding in the power button for a few seconds, then try starting it again. If that also does not work, you need to replace it.