Why can't I add any products to my shopping cart?

Normally this is caused by a conflict between a site setting and some custom coding added to the head content of your site.  In Sites > [site name] > Settings > General Info tab in the "Shopping Cart" section, check to see if you have "User must select shipping address" turned on.  Then check in Sites > [site name] > Settings > SEO/HTML tab in the "Edit HTML Head Content" area to see if you have added a code snippet to the head content to hide the ship to display on the product page.  The code snippet would look like this:

    .shipToArea{display: none;}

If both of these are present, then you are requiring the user to select a shipping address but preventing them from doing so by hiding the selection area.  You either need to turn off the user must select shipping setting or remove the code snippet from the head content.