Ajax和Google reCaptcha

Question

I'm trying to add reCaptcha to my resigration form on my website. I've followed a video tutorial on how to do it, however I'm struggling to adapt it to work with my form that use ajax to call a PHP file and does not actually submit the form. I've tried a few things suggested in previous questions, but none seem to get the intended result and instead display "I don't like robots" to the registration page. Some hints / suggestions would be nice if you can think of any.

<div class="g-recaptcha" data-sitekey="6LcXMg0UAAAAABmlDlOGa6onxqqzERZ483XOJbFm"></div>

Javascript

function Register(){
        var Forename = $("#txtForename" ).val();
        var Surname = $("#txtSurname" ).val();
        var Password = $("#txtPassword").val();
        var PasswordR = $("#txtPasswordR").val();
        var response = $("#g-recaptcha").val();
            $.post('functions/php/fncregister.php', {Forename: Forename, Surname: Surname, Password: Password, PasswordR: PasswordR, response: response}, function(data) {
                var returnValue = JSON.parse(data);
                if (returnValue['data'] == 0){
                    $('#mdlInfo').html('<p>Your account has been created under the username: <strong><span id="spnUsername">'+returnValue['username']+'</span></strong>. You <strong>must</strong> remember this as you will require it to log into your account.</p><p>Your account has also been added to a moderation que. <strong>You must wait until a member of staff activates your account!</strong></p>');
                    $("#mdlRegister").modal("show");
                }
                else if (returnValue['data'] == 1){
                    $('#divError').html('<p class="text-center text-danger bg-danger" id="pUPInc">Passwords did not match!</p>');
                }
                else if (returnValue['data'] == 3){
                    $('#divError').html('<p class="text-center text-danger bg-danger" id="pUPInc">An error occured when adding your details to the Database!</p>');
                }
                else if (returnValue['data'] == 4){
                    $('#divError').html('<p class="text-center text-danger bg-danger" id="pUPInc">I don\'t like Robots!</p>');
                }
            });
    }

PHP

<?php
//Retrieves variables from Javascript.
$Forename = $_POST["Forename"];
$Surname = $_POST["Surname"];
$Password = $_POST["Password"];
$PasswordR = $_POST["PasswordR"];

//reCaptcha
$Url = "https://www.google.com/recaptcha/api/siteverify";
$SecretKey = "---KEY---";
$Response = file_get_contents($Url."?secret=".$SecretKey."&response=".$_POST['response']."remoteip=".$_SERVER['REMOTE_ADDR']);
$Robot = json_decode($response);

$data = 0;

if(isset($Robot->success) AND $Robot->success==true){
    //OTHER CODE
}

else{
    //This code always runs (though this is only meant to happen if reCaptcha detects a robot.
    $data = 4;
        echo json_encode(["data"=>"$data"]);
?>