Hi,
I' not sure if you're telling us that the problem is that you don't see add to cart buttons, or that after you add the product to the cart and go the checkout, it says that the cart is empty.
If it's the latter, it looks more like a server issue. You can try to change the "session handler" option of the Joomla configuration and see if that helps. Also, make sure you test on another browser with another user account just in case it comes from a user session glitch. If you still have the problem, please provide a link to a product page where we can add to the cart (on all the pages I tried, there was no add to cart button).
If it's the former (the fact that the add to cart buttons don't display), it's either that you turned on the "catalogue mode" option of the configuration, or that you turned off the "show add to cart button" option of the configuration.