The Videos do play, they just don't play properly. The video will freeze or become distorted periodically, while the audio will play on. WMP plays them fine. I've encountered this before with MOV files that will only play properly in Quicktime (videos from Lynda.com, in particular).
Changing options in WMP did stop the files from opening in VLC, but they still won't open directly. The "Open With" dialogue pops up every time, asking what program I want to use to open the file. Checking the "Always use the selected program" box does nothing. It just pops back up again next time. Perhaps this problem is beyond the scope of this forum. Maybe it has to do with the fact that I've
removed the WMP context menu entries...
**EDIT**
Yep, that's exactly what it was. When I ran "regsvr32 wmpshell.dll" the problem was solved.