PHP contact form is not working - php

Question

I'm trying to add a contact form to my website but each time I click send it takes me to a black window and the address bar says contact.php. Also it doesn't redirect back.
My website is hosted as an application using the google app engine.
I tried literally everything but I can't get it to work.
Below is my HTML code:
<form action="contact.php" method="post">
<p>Your name</p>
<input type="text" name="name"/>
<p>Your e-mail</p>
<input type="text" name="email"/>
<p>Message</p>
<textarea name="message"></textarea>
<input type="submit" value="Send"/>
<input type="reset" value="Clear"/>
</form>
and here is my PHP code:
<?php
$field_name = $_POST['name'];
$field_email = $_POST['email'];
$field_message = $_POST['message'];
$mail_to = 'email#here.com';
$subject = 'Message from a site visitor '.$field_name;
$body_message = 'From: '.$field_name."\n";
$body_message .= 'E-mail: '.$field_email."\n";
$body_message .= 'Message: '.$field_message;
$headers = 'From: '.$field_email."\r\n";
$headers .= 'Reply-To: '.$field_email."\r\n";
$mail_status = mail($mail_to, $subject, $body_message, $headers);
if ($mail_status) { ?>
<script language="javascript" type="text/javascript">
alert('Thank you for the message.');
window.location = 'contact.html';
</script>
<?php
}
else { ?>
<script language="javascript" type="text/javascript">
alert('Message failed.');
window.location = 'contact.html';
</script>
<?php
}
?>

Answer 1

You need a mail server, PHP doesn't sent mails by itself. Install one first. And yea, text area is missing close tag.

Answer 2

You're missing the closing textarea tag in your form. I tried the code as contact.php on my server and it works. I agree with itachi, you need to turn on error reporting.
Why not make contact.php a full page and get rid of the redirect altogether?

Answer 3

Working fine for me. Your if else condition is not working properly if fields has no values then still it gives thank you message.