Hm, I added a product to the cart, got a warning message, then a message that the item had been added to the cart. But then going to the cart button, the cart was empty. So this is a bit borked at the moment.
The cart is totally dependent on JS, which is why you aren't getting the page load. Not sure how you set this up (is it just an out of the box template?), but personally I'd ditch this and try something better.