The reason it's going to a blank page is that the PHP page is blank! You don't seem to be echoing your success message anywhere on the page.
I would recommend changing your form so that the HTML is as below:
<form method="POST">
And then paste the PHP into the top of that page. Remember to set the page type to .php rather than .html/.htm
Finally add an echo to the top of your form so the success message will display, along the lines of
<?php
if ($success) {
echo $success;
}
?>