OK, mystery solved! It was related to plugins; specifically plugins from Topaz Labs. They
recently released updates to two of their products. In response to many
complaints about install problems they created a "utility" whose
actions resulted in my problems.
For anyone who has the same problem as me and reads this, here is the fix:
In the folder C:\Program Files\Common Files\Adobe\Plug-Ins\Elements 15 delete all the shortcuts created by the Topaz utility.
The only thing that should be in that folder is another folder named "File Formats".