Hi,
I've checked your checkout and I do see a message when I reach it. It says "Registration not allowed".
That's because you've turned off the user account creation in the settings of the Joomla user manager.
And thus HikaShop follows that setting and don't offer the registration to your customer. This means that you need to be already logged in to be able to checkout, but you've also turned off the "login" setting of the Checkout tab of the HikaShop configuration and there is no login module on your website so your customers can't login either.
Thus, your customers get stuck on your checkout with no possibility to move forward.
So either turn on the user account creation and/or allow customers to login and/or set the "registration" of the Hikashop configuration to "guest" so that customers can checkout without a user account (this requires a commercial edition of HikaShop)