What I mean is that if you visit all of the 14 PHP files you listed that exist in the directory, some of them show a vBulletin-like page (even if it's just an error message). This is the correct behavior, and it means your rewrite rules are working correctly. So it's not a rewrite issue. However, if you visit certain others of those files (such as ckeditor.php), you get absolutely nothing, just a white page and a 200 OK status.
Usually a white page is indicative of a fatal PHP error, but if display_errors isn't showing one, then the page is dying for some other reason (e.g. it's hitting an exit or die construct somewhere).
I've added a service to your Members area. If you can fill it out, I can inspect the files on your test site and try to find where this is happening.