Why does this not work?

[Joe Lowder]

For years, I have used bluemail form input for a simple
way to invite comments from visitors to my websites;
but recently discovered that this quit working:

http://www.upquick.com/message/

So, I asked bluehost support for a remedy and they
sent the code sample shown below, which I uploaded
to a test site: upquick.com/message/forminput4.htm
to try to use, but it does not work.

What do I need to change to get this to work?:

<!-- forminput4.htm 1912-29 -->

<?php
//if "email" variable is filled out, send email
 if (isset($_REQUEST['email'])) {

//Email information
 $admin_email = "joe at actionline.com";
 $email = $_REQUEST['email'];
 $subject = $_REQUEST['subject'];
 $comment = $_REQUEST['comment'];

//send email
 mail($admin_email, "$subject", $comment, "From:" . $email);

//Email response
 echo "Thank you for contacting us!";
 }

//if "email" variable is not filled out, display the form
 else {
?>

<form method="post">
Email: <input name="email" type="text" /><br>
Subject: <input name="subject" type="text" /><br>
Message:<br>
<textarea name="comment" rows="10" cols="40"></textarea><br>
<input type="submit" value="Submit" /><br>
</form>
<?php
 }
?>