I just want to get this straight, the problem is when you are viewing the site using http://localhost/ instead of http://www.domain.com and its with vbulletin.
i didn't think reinstalling the server would had been the solution. Try reinstalling vbulletin. 🙂
why don't you backup your local server vbulletin files and copy the files from the 'live' site.
Also, is your broswer accepting cookies? that could be the issue.
Last option, i can think of, if your localhost server is also serving the public website, then look at the vbulletin files and search for "setcookie", look at how its used, then read the php manual on setcookie to understand what i'm saying.
i'm sure that when it creates a cookie (using the php function "setcookie()") its restricting it to the .domain.com so when you log on it (via localhost) won't remember the cookie set by vbulletin. Could be absolutely wrong though.
(could be sending you on a wild goose chase. This is how i would have approached this problem, though)
hth.