I've just tried logging in and out of your board using the supplied data and had no problem whatsoever on both logout links. The logout procedure just deletes the site's vB
cookies, nothing else. The code is fine, I see no problems at all.
So, if the code is ok and no other pcs and browsers share your problem, then the problem is your browser (or in your browser). Maybe the old site phpBB2 cookies are messing with the new one...
That said, replacing vB
files won't do a thing. What you need to do is try a different browser. Download and install Firefox. Try to log in and out of your site and see if you have the same issue.