Hi, it sounds like there's an error occuring when adding to basket. Perhaps this isn't showing because of a customisation either with the theme or through third party extensions.
Are you familiar with the network tab of the developer toolbar in Chrome/Firefox? This should allow you to view what happens when you hit add to basket and see if you are getting a positive response or not.
Changing the default theme temporarily is another way of ruling whether it's a theme issue or not.
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