Cumulative Update for Windows 10 (KB3147458) breaks Explorer, Start Menu, desktop, apps

After installing KB3147458 today, Explorer, the Start Menu, my desktop, and all my non-Win32 apps broke.

Here are the problems:

Clicking the start menu does nothing. Pushing the Windows key does nothing.
Clicking the search icon on the taskbar does nothing.
Clicking the show desktop button on the taskbar does nothing.
Trying to open Calculator gives an error: "Explorer.EXE Class not registered". The Calculator icon on my taskbar does not render.
Trying to open Control Panel via Run gives an error: "::{26EE0668-A00A-44D7-9371-BEB064C98683} No such interface supported"
Trying to open folders via Run gives an error: "[File path here] No such interface supported"
shellexperiencehost.exe does not run
Windows Photo Viewer does not open. Thumbnails for images on the desktop do not render.

Before the update, I was unable to open the MSN News and MSN Weather apps. I have a feeling that the security patches for IE and Edge have something to do with these new problems.

https://www.reddit.com/r/Windows10/comments/4egyrg/windows_10_april_updates_kb3147458_and_kb3147461/d21ld7a

http://answers.microsoft.com/en-us/windows/forum/windows_10-update/microsoft-wants-to-know-anyone-seeing-issues-with/8cc2af67-d1ef-43d8-8658-b5c5a69be530?page=13&msgId=479bbfe1-0e43-4f5c-ae51-ace73d6fcd76

Any fixes?

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