Post data to PHP file from HTML form where value of input types are set using jQuery's .val() function

Link to checkout the form Here's what i tried in Jquery:

$('#third_n').bind('keypress click',function(){

    $('p#p_service').text($('#id_service').val());
    $('p#p_rate').text($('#id_rate').val());
    $('p#p_imei').text($('#imei').val());
    $('p#p_device').text($('#id_device').val());

    var a= $('#id_device').val();
    var b= $('#id_rate').val();
    var c= $('#id_service').val();
    alert(a);
    alert(b);
    alert(c);
    });

Her's the part of jquery code that set the .val() function

var ser_val = $('#ssamsung').val();
$('#id_service').val(ser_val);
$('#id_device').val('iPhone 5');
$('p#rate').text($('#id_rate').val());

And my corresponding HTML:

<form class="nobottommargin" method="post" action="shop_paypal.php">

<label>IMEI: <small>*</small></label>
<input type="text" value="" class="required input-block-level"  id="imei" maxlength="15" required/>
<label>Cost:</label>
<input id="id_rate" type="hidden" name="na_rate">
<p id="rate"></p>
<label>Notice:</label>
<p id="p_notice"></p>
<label>Details:</label>
<p id="p_details"></p>
<label>FIRST NAME:</label>
<input type="text" value="" id="FN" name="first_n" required/>
<label>LAST NAME:</label>
<input type="text" value="" id="LN" name="first_n" required/>
<label>EMAIL: </label>
<input type="email" value="" id="EML" name="first_EML" required/>
<label>Device:</label>
<input id="id_device" type="hidden" name="na_device" value="">
<p id="p_device"></p>
<label>IMEI:</label>
<p id="p_imei"></p>
<label>Service:</label>
<input id="id_service" type="hidden" name="na_service" value="">
<p id="p_service"></p>
<label>Rate:</label>
<p id="p_rate"></p>
<label>Name:</label>
<p id="p_name"></p>
<label id="l_email">Email:</label>
<p id="p_email"></p>
<input type="submit" class="simple-button large" id="submit">
</form>

Till here every thing is fine, getting right alerts via jquery and the text correctly gets set in<p> tags.

But this Corresponding PHP Code echoes nothing:

<?php
session_start();
   $rate = $_POST['na_rate'];
   $device = $_POST['na_device'];
   $service= $_POST['na_service'];
   $email = $_POST['first_EML'];
   echo $email;
   echo $device;
   echo $service;
   die(0);

I'm not sure why? Any help is much appreciated. Thanks