What do you mean it appears to restart? It either does or it doesn't.
Shut down computer, not restart. Then boot the computer. Then don't do anything on your computer, nothing. If Windows updates were downloaded and not completely installed it should do it now. If Windows informs you updates were installed reboot whether Windows ask you to or not. If this doesn't work open Windows updates and manually check for updates. If the previous updates didn't install Windows Update should recommend them again.
Let us know what happened. My rules on my computers is simple. 1/When downloading and installing Windows Updates do nothing else on the computer, period. 2/ Check for updates manually 2 to 3 times a day. 3/ If there is a big download of several KB's like on some Tuesdays take a few at a time reboot and do it again. 4/ Have I.E. set as your default browser for updates. Microsoft likes Microsoft. This may help from having problems in the future, it did me.