Finally solved the problem...  must less complicated than I thought.  I merely needed to change the display once.  I changed to my TV for a day, and when I switched back to my monitor all of the videos played correctly.  Thanks to anyone who spent even a second thinking about this problem!

The videos and animations were working correctly.  However, after changing the order of two videos to match the text in the "Smiles" Story Time section, I quickly cycled through the story in LR, pressing 'Enter' rapidly until I reached the final two slides I corrected, and then suddenly the videos began to play in a cropped state.  Now, only the upper-left section of the videos play, with the bottom and right sides cropped showing only black screen.  The files themselves are fine, as all of the videos play correctly in other media players.  It is only when they play in LR that they are cropped (though rarely certain videos or animations play back correctly).

I have already tried repairing/uninstalling-reinstalling LR.  Didn't work.  I also repaired the .NET Framework and Flash Player.  Didn't work.  I also downloaded the K-codec pack and the FF codec pack.  Didn't work.

If someone has any idea how I can fix this problem, I would be enormously grateful for your help!