Hi,
We uses the official Joomla popup systems.
Your template should be compatible with at least, one of us.
It is possible that your CSS is not compatible with the Joomla popup, but it is possible that your configuration not right and HikaShop does not try to open your popup.
So, when you are in the checkout, can you edit an address in a popup ? If you click on the "modify" icon, a popup for the address will be open. At this moment we will be able to know what is exactly the problem (or, having a better direction to search).
The other good idea will be to provide a link to your website so we can take a look.
Regards,