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: Yes, I know it can be a pain to remove batteries from a tablet (not impossible, just a hassle). Due to this, if your tablet is still under warranty, be sure you contact the manufacturer first, before doing anything physically to the tablet. Don't want to void the...