You should copy the code for the form from the default vbulletin template because it will include the security token in it.
Did you use the 'template' in the article for
How to create your own vBulletin-powered page! (uses vB templates) to start your new page? You might want to read that article. I think you need to include a new line about the security token in the php page. Take a look in that article and see if it's mentioned.
edit: This article tells you what to put at the top of your page to deal with the security token -
Implementing CSRF Protection in modifications