Hi,
At the time of this writing no HikaShop JS or CSS is being loaded on your pages, and there is no indication of, or link to, a cart or checkout So, to begin with, could you please download the very latest version and re-install it over the present one for the necessary core files to be present and work?
If then problems with the checkout would still persist, it'd be good if you could post screenshot(s) of the configuration of the checkout in the HikaShop backend.
P.S.:
Just notice that the "Shop" link in the main menu as well as product listing/pages are gone now. You seem to be still experimenting? Please come back here when done, so there is something to see without being changed short-termed.
You may then as well post here a "hidden" shop link from a menu which is not published to any position.