Well I'm hoping that rolling back the PHP version fixes it, or else that we can live with it. As I said I never even knew about the new post page. I just scroll down through the main forum page and look for a "New Post" icon next to a sub forum and that always worked for me, although I can see how the new posts page would be convenient.
I contacted vBulletin about upgrading, and we could upgrade to version 4, which is compatible with the latest PHP versions (assuming that this issue really IS related to the PHP version). The rub is that I don't have the credentials for the vBulletin license since Mike never gave them to me before he passed, so I'd have to buy a full license for $249 (not that an upgrade is all THAT much cheaper at $209).
That's a chunk of change. I think I'd rather try to setup an open source PHPBB forum instead and convert the forum database (there are free conversion utilities out there). PHPBB is basically an open source version of vBulletin - forked from the same code base way back.
Ironically, tech support says our version of vBulletin should not even work with the previous version of PHP we were using (5.4) but I went back through my notes and back in 2012 the web host upgraded us to 5.3. It broke a LOT of things and we were getting all kinds of errors. I wound up having to make some changes in the PHP variables declarations that were suggested on the vBulletin support forums, and the web host had to disable "reporting of deprecated messages" in the PHP.INI file. That fixed all the problems, and I guess that hack also allowed it to work under PHP 5.4.
So everyone keep trying the New Posts page and let me know if it's working now. I'll keep my fingers crossed.