you have configured the discount to apply only if item ID 1 is in the cart.
it will only apply the discount if the item being added to the cart has an ID of 1.
your cart page is giving the following error when the checkout button is pressed:
Warning: Cannot modify header information - headers already sent by (output started at /home/content/59/7662459/html/cart.php:86) in /home/content/59/7662459/html/cart.php on line 89
this means there is a problem at line 86 of the cart.php page.
see the following thread for details on the headers already sent error and how to correct it: