While I have been searching Forumotion support files for the last two days, it appears that DFC has uncovered more than I did. As we suspected, it does not appear that any settings on our own forum have caused the problem with the display of Photobucket-hosted images. There may be something at play with our host Forumotion or with Photobucket and the way in which they interact. As indicated in the previous post, DFC has written a dedicated message to Forumotion support on this issue and we are awaiting a response. I am sure some sort of fix will appear, but none of us know how soon this will be. Please bear with us. If you are up to it, consider looking into other image hosting sites. Imgur, Flickr, and Servimg (which is somehow associated with or recommended by Forumotion) all appear to work. For what it is worth, I opened free accounts in the latter two when I started this forum, and so far have run into no issues.
On a personal note, having infected my computer with malware while installing Chrome to replicate that browser's experience (in vain), I may be a little distracted in the immediate future.