The problem is that you've put double quotes around strings that contained double quotes, so they're mismatched. If you use single quotes instead it should work, like:
Code:
$banner[1] = '<a href="http://bham-jk.com/showthread.php?1015-Meet-N-Mod-Party" target="_blank"><img src="http://i93.photobucket.com/albums/l72/JOHNNYP4409/MeetNModparty_zps9e808cc0.jpg" border="0" alt="MeetnModParty"/></a>';
$banner[2] = '<a href="http://www.tntaccessoriesnservicecenter.com/" target="_blank"><img src="http://i93.photobucket.com/albums/l72/JOHNNYP4409/TNTBannerBlack.png" border="0" alt="TNTaccessories"></a>>';
$rotator = rand(1, 2);
$bannerrotator = $banner[$rotator];
vB_Template:: preRegister('navbar', array('bannerrotator' => $bannerrotator));
Also I noticed that the $banner[2] string has >> at the end, I don't know if that's a typo or not.