It sounds like there may be something on the tablet that shouldn't be. Virus, malware, bad app, etc. Try starting the tablet in "Safe Mode" and see if it will turn on. If it does, then I would be looking for uninstall any recent installs or recent updates, and also running virus and malware checks on the device.
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.