I had to change the player's global security settings on all computers to get them to play anything local, which worked on all but this computer. I've learned that from outputting files to local sites and testing them locally. So, that's been done for some time.
I've tested this on four different browsers, and also by simply doubleclicking the start.swf file, all with the same results. The individual .swf files load (evidenced by the menu on the right "filling out").
I must say that the loading procedure on this computer is much more halting than other computers, which seem to load smoothly. It seems to try to load every movie (for one second of play each) before the menu fills out and it presents the starting movie, again, for "play".
Pressing the play button on any menu lesson results in about one second of advancement in the progress bar, then nothing. However, if you do press the play button on any movie, that's the last play button you will see. From then on, there is no more play button on any "lesson", instead the progress bar is one second in to the movie, and the "stop" button is presented (rather than "play").
Again, if I had no options to see these movies, I might be more upset, but, as I said, I can watch them on other computers, so I'm not feeling cheated. I also think it might be a waste of resources to occupy someone's time at Webassist troubleshooting this problem. Webassist, after all, did not produce flash player.
After all, it can't be the files, they play on other computers, it can't be flash player because it plays any other file (local or remote), and I've combed through my firewall and browser settings just in case (all of the pertinent applications are enabled).
My first thought was that maybe captivate produces a particular "flavor" of .swf file that flash player, on this computer, couldn't play. That seems a bit of a stretch.
Anyway, thanks for the suggestions, I'll keep you posted if things change.