Have you tried opening them in iMovie? the might yield a clue as to what is going on.
I gave iMovie a try but it just made things more mysterious. When using "Import Movie" it shows some files as greyed-out and others as apparently openable. However, iMovie won't open all files that would seem to be okay. Instead some open and some have a -37 error. Quicktime, on the other hand, will open every file with an icon that appears to say okay.
At this point I think I should try the various pieces of software (VLC, Handbrake, et cetera) and track the differences. Maybe a more comprehensive list of results will be more helpful.
