As you advised, I used SFC and it found no errors.
I found a simple work around. I just put a copy of explorer.exe from another computer in my documents directory and it works fine, That will do until I upgrade to Windows 10...after it is out a while.
In my case, right clicking on a file or folder on the right pane of Windows Explorer produced the context menu, as expected. However, doing so on the left pane caused WE to reset.
The culprit was a plugin in SpyBot Search and Destroy (Advanced Tools > System Integration > Windows Explorer Integration (64 bit)). Once I uninstalled it, WE started to behave correctly on both panes.
I finally solve this under Windows 7 by moving a second copy of explorer.exe to a different directory and using that. Why that should work I have no clue. I'm now using Windows 10, oh whoa, and explore is not a problem