One idea would be to look at the showbanner.php file and see if $db->query_read_slave or $vbulletin->db->query_read_slave appears within a function. If so, globalize $db or $vbulletin near the beginning of the function:
Code:
global $db;
global $vbulletin;
Another idea is to look at the code from the /home/beta/public_html/index.php file, around line 394 to see what it is doing. Seems like a scope issue, i.e., a variable needs to be globalized, but without more info, it's a guess.