Well technically the battery should be removable, just no one said it was something you could do easily.
Why they make it so frustrating I don't get. Make sure you leave it unplugged while you let the battery drain.
Once it is totally out of power, charge it while off. Then when you go to turn it on, be sure to start it up in "Safe Mode" and see if it will shut down fine from that. If yes, you have something on the device that you need to remove/uninstall.
How to enter "Safe Mode" when booting the computer.
In Windows 8 and 10 ...
As your computer restarts, press F8 (possibly a few times) to enter "Safe Mode"
a. Press the "F4" key to Enable "Safe Mode".
(The computer will then start in "Safe Mode" with a minimal set of drivers and services.)
b. Press the "F5" key to Enable "Safe Mode" with Networking.
( Once "Safe Mode" with Networking starts, Windows is in Safe Mode, with additional network and services for accessing the Internet and other computers on your network.)
c. Press the "F6" key to Enable "Safe Mode" with Command Prompt.
(In "Safe Mode" with "Command Prompt" starts Windows in Safe Mode, with a Command Prompt window instead of the Windows interface. This option is mostly only used by IT professionals.)
Now sign in to the computer with your account name and password. (If you have one set.) When you are finished troubleshooting, you can exit "Safe Mode" restarting your computer.