If you click the links in the header you'll see that everything works fine, short of accessing:
http://www.byzcath.org/forums/ubbthreads.php
http://www.byzcath.org/forums/ubbthreads.php?ubb=cfrm

Could you load this PHPInfo (only that link as it has additional data appended to it) page and tell me if the value for "PATH_INFO" is "/test"? I'm thinking it should work, since I can access:
http://www.byzcath.org/forums/ubbthreads.php/forum_summary

I'm trying to figure out why the server isn't passing a variable, if we can't get it figured out you may just have to roll back to PHP5.6 for the time being.

You don't happen to have a .htaccess file in one of these directories that has any sort of apache redirect or 301 redirect in place?
/home/byzcatho/public_html
/home/byzcatho/public_html/forums/

Is there any entry in your web server logs which mention the forum folder?

Did your upgrade to UBB.threads v7.7.0 complete through all of the transition steps?

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