Apparently the problem is with the vBulletin forum software that we run. The company that bought the software and develops it has proven itself to be professionally incompetent and devoid of any responsibility to its customers. Apparently they knew a long time ago that the software had become incompatible with the latest versions of the programming language which is needed to be loaded in order for this website to run (PHP). Now this software is only compatible with unsupported versions of PHP - yes, you read correctly. They were so irresponsible that they let the software have bugs so that it doesn't work with any supported versions of the core software it needs to run (probably to focus efforts on developing more products to sell.)
At this point the fix is going to be more than just a night's work, which I thought meant an upgrade. It also involves someone with better PHP skills than myself, whom I'm going to hire and get fixed since the company doesn't even have a bug fix firmly on its agenda.
I mentioned earlier that I anticipated moving our forum to new software and had thought it would have been done earlier. Given that so much of the site was integrated, I wasn't sure it was a good idea. Now that it's clear that this beloved software has become a liability, the move may take place sooner than anticipated. I think you'll love either of the two solutions we anticipated using.