Looking at the source code for that area, I see you've got a number of improperly nested tags in that area. I wouldn't be surprised if that was mucking up the log in. The Validator reveals quite a few errors in the logged out version of the page:
http://validator.w3.org/check?uri=ht...e&group=0&ss=1
Try going though that list of errors, starting with the top most one, and work your way down. Then revalidate your site each time until you've got them fixed. Errors cascade, so fixing one might fix others, but at least if you fix them, you'll be able to rule that out. You can tell what area in the code is what by going to your
vBulletin Options >>> General Settings >>> Add Template Name in HTML Comments. Then the template names will appear in the source code.