Update: I played around with the demo cart to find what URL it should be going to. (It seems that it just changes "cart" in the url to "step1")
I manually typed in the path to where the checkout should begin, after adding something to the cart: http://www.goldmanskosherbakery.com/OnlineStore/tabid/68/ctl/step1/mid/393/Default.aspx
After doing this, it looks like the checkout process was going normally. It just seems like there's an error in the Checkout button itself (maybe the AJAX?)
If anyone knows what to do, it would be much appreciated!
Thanks again.