Have you tried turning it on in "Safe Mode"? If not, I would try that. The reason being if it was a bad app, malware, virus, etc., that caused the problem, you may be able to get it to turn on this way. In "Safe Mode" you can't do a lot of things, as it is a restricted mode, however you can then uninstall anything recently installed (or updated) and remove anything else that could be the cause, then reboot to see if it will start up fine.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.