I had the same issue, and I managed to solve it.
The Problem: At shutdown, Windows would simply hang up, displaying the "Shutting Down" screen indefinitely.
The Cause: I own a "ZBoard", a particular brand of gaming keyboard. I've owned the keyboard for several years, and in that time the company which originally made the keyboard was bought out by a different company. The new company put out some new drivers/applications which were updated by Windows, which did not jive with the older version of the drivers/application already on my computer. For some reason, this caused the shutdown hang up (don't ask me why, I'm not sure).
How I Found It: I noticed after my last update that the ZEngine was included. Furthermore I ran a System Health Report (found in the following directory: Control Panel -> All Control Panel Items -> Performance Information and Tools -> Advanced Tools -> Generate a System Health Report) and saw that my ZEngine drivers were not working properly.
How I Fixed It: I then uninstalled the old ZBoard application and drivers, and installed the new ones from the site. Now it shuts down and restarts like a dream.
I hope this was helpful. Just so you know, I am NOT an expert, I'm just determined and had about three hours of extra time on my hands; so PLEASE do not ask for advice... I only posted it on the off-chance that it may help others in my situation, or be applicable to other reasons why this phenomenon may be occurring.