Can you copy and paste the original code in your page? There is a reference to javascript and other code that is different, so that could be part of the problem.
Also, I wonder if the <form action="" needs to have an entry? Maybe not, but thought I would throw this out there.
The forms that I do, I have the php in its own file named "feedback.php," so my code is: <form action="feedback.php" method="post"> and it calls the php file to execute my forms. And the actual page that has the php code is named form.php. I have CAPTCHA on mine, too, but that isn't something that everyone does.
Here's an example of a request form from a roofing co site I did:
http://www.hsroofingco.com/form.php If you click the submit button without entering all the required info, a page will pop up and tell ya.
It's a little separate HTML page - also a little HTML page comes up if they submit everything perfectly and they can go back to the home page from there.
If you try it out, PLEASE don't fill out the form correctly, because it will go to the owners of the company - and they might not appreciate that! You can click the submit button without filling anything out. 
ETA: Codehead could be right about your host.
Re: Dreamweaver code
Linear Mode
