Tank Girl,
Did you check the links I provided in the PM? Those are from Forumotion's resolved support threads. I found a third, but it seemed even less helpful.
I have experimented with any changed settings to this forum, and reverting to earlier settings (which had nothing to do with gifs anyway) did not make a difference with the display of these images.
Have you made changes to any of your settings or preferences here? Or on Photobucket? I know from flickr that if you simply change the status of an image to private or public, the whole link changes, although I doubt this is the issue here.
From the start I have pointed out I am not tech savvy and I call upon the other Founding Fathers and other forum members in general to find us a tech and/or a solution.
I hope this is worked out, as it is truly a curious and disturbing issue.
PS A logical step would be for anyone else with Photobucket to test this and see if their images (jpeg or gif) from there would display here.