PHP/Javascript Contact Form Not Working

I have a contact form on a Wordpress based website that is not working. It works on the theme creators site, and I have tried to contact them for help, but have not received a response.

If you can help I will be truly grateful.

THEME DEMO PAGE (it works here): http://vooshthemes.com/gallery/satoshi-v2/?page_id=14

Here is the code for the 2 files

JS file

$(function(){
	$('#form_submit').click(function(){
		
		var input_name = $('#form_name').val(),
			input_email = $('#form_email').val(),
			input_subject = $('#form_subject').val(),
			input_message = $('#form_message').val(),
			response_text = $('#response');
		
		response_text.hide();
		response_text.html('Loading...').show();
		
		$.post('http://www.justicewebdesign.com/wp-content/themes/satoshi/scripts/contact-process.php', {name: input_name, email: input_email, subject: input_subject, message: input_message}, function(data){
			response_text.html(data);
		});
		return false;
	});

});

PHP file

<?php
if(isset($_POST['name']) && empty($_POST['spam_check']))
{
	require 'email-validator.php';
	$validator = new EmailAddressValidator();
	
	$errors = array();
	
	$input_name = strip_tags($_POST['name']);
	$input_email = strip_tags($_POST['email']);
	$input_subject = strip_tags($_POST['subject']);
	$input_message = strip_tags($_POST['message']);

	$required = array('Name field' => 'name', 'Email field' => 'email', 'Message field' => 'message');
	
	foreach($required as $key=>$value)
	{
		if(isset($_POST[$value]) && $_POST[$value] !== '') 
		{
			continue;
		}
		else {
			$errors[] = $key . ' cannot be left blank';
		}
	}
	
    if (!$validator->check_email_address($input_email)) {
           $errors[] = 'Enter a valid email address.';
    }
	
	if(empty($errors))
	{		
		if(mail('contact@justicewebdesign.com', "Message from $input_name - $input_subject", $input_message, "From: $input_email"))
		{
			echo 'Thank You - your email has been sent.';
		}
		else 
		{
			echo 'There was an issue when sending your email. Please try again.';
		}		
	}
	else 
	{
		echo implode('<br />', $errors);		
	}
}
else
{
	die('You cannot access this page directly.');
}

hmmm. still no solution

Martinfamily2005 I know this sound elementary but have you included the line to load the JQuery scripts in your html file. Remember it must be before any Javascript files that need to load as well. Also could you give anymore details of the errors you are getting. Is the data not being posted or are there database errors that or occurring?