I have products defined and listed. I can add items to the cart, but when I click on the 'Checkout' button nothing happens.
UPDATE: This product which never goes to the checkout was actually a Copy/Edit of an existing product, and that existing product has no problems with the check out. So I am assuming there was a problem with the database when I created a copy. I'll just delete this problem product and build its replacement from scratch.
I think the reason because the product is out of stock so it can not be checked out. You should go to EShop -> System -> Configuration -> Option tab, at Stock Checkout choose Yes, then Save the configuration and test again.