When you can't get your computer to shut down, it could indicate a currently active application needs to complete a process or stopped responding. This can happen whether you instruct the computer to shut down or restart. When nothing seems to work, you can try various troubleshooting steps, from quitting currently active applications using the Task Manager to the last-resort option of manually shutting down your computer.
Hibernation and Sleep
Windows 8.1 uses hibernation and sleep mode to save your currently active applications and documents to make it possible to get back to work quickly. You could have Windows set to hibernate or sleep instead of shutting down when you press the shut down icon. Point your mouse at the upper-right portion of the screen and swipe down to activate the Charms bar. Choose "Settings," type "Power Options" and select "Power Options" from the list. Select the "Choose What the Power Button Does" option and select the option to shut down your computer. Now when you click the shut down icon, it should shut down your computer.
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Sometimes an application prevents you from shutting down your computer when it stops responding. You can correct this issue by closing the errant application. Press "Ctrl-Alt-Delete" and click the "Task Manager" link to launch the application. If that doesn't work, try right-clicking on the taskbar and selecting "Task Manager" from the list of options. End any of the currently active applications toward the top of the list. Once you successfully quit the applications, attempt to reboot or shut down your computer again.
High CPU Usage
When you can't close an application that stopped responding, try to free up system resources so that the application begins responding again. Select the application and choose the "More Details..." arrow. Click the "Processes" tab. Look for the apps using the greatest amount of CPU cycles, select them and click "End Task." Close as many applications as you can to free up resources to end the application causing the problem.
The final option, the hard shutdown, forces your computer to shut down by cutting its power. You should avoid this option unless all other troubleshooting measures failed to work. Using this option can cause errors with any currently open applications, causing you to lose data and possibly corrupting system files. Before going through with the hard shutdown, wait an hour or so to see if your computer starts responding. If it doesn't, hold down the power button until the computer shuts off. In an absolute worst-case scenario, you can unplug the power supply to the computer. After a hard shutdown, your computer usually runs diagnostic tests to verify the integrity of the file system.