Have you tried holding the power switch down for 20 or 30 seconds (or until something happens, if it happens sooner)?
If that still gives you no results, try getting it into download mode (Volume Down + Home + Power) (until you get the warning screen, then volume up to download mode). If you can do that, you can use Odin to reflash the ROM (see [Samsung] How to flash Stock ROM via ODIN). (Your data will already be gone, so there's no data you can lose.)
If you can't, you'll have to bring the tab into a repair shop and see if it pays to repair it (depending on which one you have - size and amount of storage, they appear to be going for $100-$200 new) or replace it. (In other words, if it's a 7" with 16GB of storage, and the shop wants anywhere near $100 to repair it, buy a new one.)