double check your index.php page has session_start();
try doing a var_dump() on both $cart and $_SESSION['cart']
var_dump($cart);
should return:
---------------------------
object(ShoppingCart)#1 (0) { }
var_dump($_SESSION['cart']);
should return:
-----------------------------
array(2) { ["totPrice"]=> int(0) ["totKorting"]=> array(3) { ["totaal"]=> int(0) [6]=> int(0) [19]=> int(0) } }