I have never experienced this issue. I've two hosting accounts, one with godaddy, and something with hostgator. You will find identical files on both of these Web addresses:

http://world wide web.cloth2clay.com

and

http://world wide web.vitaminjdesign.com/cloth/towels/

Both websites look exactly the same, but there's one major difference. When completing the contact page around the second link, it really works properly and will get delivered to me. One the very first link, you press submit, and also the success message does not appear and also the mail isn't sent. It does not work! The files are the same. it can make no sense in my experience. The contact page is PHP and ajax. Possibly its something on godaddys after sales? Any ideas?

Odds are the configuration configurations (or perhaps the version) for PHP and/or its modules differ between your two hosts. Try developing a script which has just the following inside it:

<?php

    phpinfo()

?>

And viewing it inside a browser after that you can compare the configurations for.

the mail isn't sent

You are contacting the shape? I am speculating GoDaddy does not support mail().