Hi,
I don't understand.
If you don't display any product in your website when the cart is empty, how could someone put a product in his cart ?
The link you provided is a link to a product listing, the goal of the product listing is to link products (even if the cart is empty).
So I really don't know how the product listing could not list product in the conditions you want (except you do some view override in HikaShop to introduce such feature).
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.