Windows Update Hangs Problem Solution

First, is the time and date right on your PC? Microsoft has a "Fix It" file available on its support page that talks about this issue, Article ID 2700567. Just run that, and it may fix your issue. If not, you may have to use System Restore to reset Windows to before it hung on Windows Update. In Windows 8, you get there by restarting your PC, clicking the power icon on the login screen, holding down the Shift key, and selecting Restart.
That will load a screen with some troubleshooting options. Select Troubleshoot, then Advanced Options. When you click System Restore, your PC will reboot in the Restore mode. Select your account, select Next on the next screen, choose your Windows drive, hit Next again, then wait for the restore process. You can hit Restart when that's done, then redo Windows Update.

If your system isn’t booting in Windows 7 and you need to restore, you need the installation disc and access to an admin account (home desktop users have this account type by default). Pop in the disc, reboot, and press any key when your PC prompts you to (shortly after the POST, but before your current Windows installation would start loading). Click through the CD's language, time, and input settings, select "repair your computer," and follow the onscreen instructions. The most recent Restore Point should work. After this process reboots your computer, try Windows Update again.