Modify existing AJAX/PHP/HTML form submission to work with Facebook App (FBJS)

We are building a new Facebook fan gate page that includes a HTML form where users can submit their name and email address in order to enter a competition we are running.

We have managed to get everything working properly using a standard AJAX script (attached) and a PHP script (attached) remotely hosted on our server that validates the fields. However, when we try and implement this in our Facebook page (we are using the Static HTML App from Thunderpenny to post our code), the mail is still sent, but the AJAX callback function is not working, so the user does not know that the form has been submitted, or if there have been errors.

We have tried implementing some FBJS sample scripts we have found online (see attached), but these have proved unsuccessful.

We are looking for someone to provide a working and fully tested FBJS code that can work with our form so that form submission notices are displayed on the page without having to load an alternative page.

To reiterate, this must be able to work within Facebook using the Static HTML App from Thunderpenny.

If you have any questions, please don't hesitate to get in touch.

Thanks.