Hi Josh,
You may press and hold the power button to force shut down the computer. Once done, restart your computer and then initiate the Windows update process and check if the issue persists.
If the system exhibit same behavior, you may follow the steps below:
1) You may follow the instructions from the following link and see it issue persists: http://bit.ly/TgKdY6
2) If the above steps does not work, you may run System Update Readiness Tool: The tool scans for inconsistencies on your computer and fixes them as it's being installed. You may follow the steps below:
• Swipe in from the right edge of the screen, and then tap Search. (If you're using a mouse, point to the upper-right corner of the screen, move the mouse pointer down, and then click Search.)
• Type command prompt in the search box.
• In the list of results, swipe down on or right-click Command Prompt, and then tap or click Run as administrator.
• In the Administrator: Command Prompt window, type the following commands exactly as they appear. Press the Enter key after each command:
DISM.exe /Online /Cleanup-image /Scanhealth
DISM.exe /Online /Cleanup-image /Restorehealth
• To close the Administrator: Command prompt window, type Exit, and then press Enter.
• Run Windows Update again.
3) If the issue is not fixed by System Update Readiness Tool, you may run a SFC scan on your computer by following steps from link: http://bit.ly/70gbQ
Although the link says for Windows vista and 7, you will be able to run SFC scan in Windows 8 as well.
Hope this helps.
Thanks and Regards,
Chinmay S