Try cutting the power (or let it run out of power to get it to actually turn off) then charge it only partially, while it is still off. After a quick charge (not a full charge) try turning it on in "Safe Mode". It will not allow access to all apps, but you can test if you get any issues while in that mode. Then try turning it off. If it works fine (minus the lack of app access) and turns off fine from "Safe Mode", then you have a virus, malware, bad app, etc., on the device that needs to be removed before you can use it normally.
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.