Hi,
With your account, when I test, I get some XML back from the server before the normal response from HikaShop:
monosnap.com/file/anz6An7DW4eje0A4j4ToOctNU4KXqo
Because of that, the javascript of the add to cart system doesn't know what to do and thus it doesn't display anything.
It's apparently some debug data from a shipping plugin commented out but still displayed on the pages.
I would recommend to remove that debug data and it should work just fine for you too.
I guess that you must have added it to be displayed only for your user account, or only for some addresses, or something like that which is why I didn't had the issue with the other user account.