Hi,
The "finish" button on the checkout can only be accessed after you login.
But from what you're saying, it seems that you're talking about the "proceed to checkout" button of your cart module.
And indeed, that button doesn't work.
However, that cart module isn't the default cart module of HikaShop.
It has been customized in some way and I'm almost sure that the issue comes from that.
Either you're using another module than the "hikashop cart module" ( and you want to contact the developer of that module for that issue), or the HikaShop cart module is customized by your template (and you want to contact your template provider).
Supposing that it comes from a customization of your template, if you rename the file "templates/YOUR_TEMPLATE/html/com_hikashop/product/cart.php to something else, that will deactivate the customization of your template and the button should then work since it will be the default button of the HikaShop cart module.