Hi,
Your problem is not limited to HikaShop.
If you check the links of your Joomla login module, on the sidebar of your homepage, you can see the same problem.
For example, the registration form page links to
combatbrick.com/component/users/?view=registration&Itemid=102
which displays that same 404 error because the index.php is missing from it.
But if I add it, it works:
combatbrick.com/index.php/component/user...istration&Itemid=102
So this tells me that you must have activated the "Use URL Rewriting" setting of the joomla configuration but didn't rename the .htaccess file and thus all the links end up without the index.php and fail as there is no .htaccess file to catch them.
And I suppose that you circumvented the problem for the categories and products for which the links work, by manually adding the index.php par to the canonical URL.