Try the following and see if it will turn on.
1. Remove the battery.
2. Press and hold the "Power" button for 20 seconds.
3. Now put the battery back in.
4. Plug it in to charge and allow it to fully charge before turning it on.
If this doesn't help, then test the charger cord to see if it is good. Either try your cord in another device, or try another devices cord on your device.
Should that not be the problem, then check the battery to see if it needs replacing.
NOTE: The battery is removable, just not easily on many tablets. If yours requires work to get to, first make sure your tablet is no longer under warranty. If it is still under warranty, then contact the manufacturer about a repair/replacement.