It’s hard to tell, but I’d first make sure that your host supports PHP.
Your form is submitting to a ‘form.php’. I assume this is the form that processes and mails the request? It doesn’t look like this file is there when I tried to submit the form?
You might check with your host to see if they have some mailer scripts that you can plug in easily. Otherwise, if you can confirm that you can use PHP, then I’d Google PHP Form mailer… There are hundreds out there that you can use as long as you attribute the author in your code.