Checkout looping between Shipment and Payment

I see that there is still a javascript error for another piece of code for the same reasons.
Could you do the same change in the file administrator/components/com_hikashop/helpers/cart.php and try again ?

Now I see again the problem as if you didn't do the modifications in the components/com_hikashop/views/checkout/view.html.php file.
Are you sure that you didn't reverted the modifications there in some way ?

Here is the file with the modifications already applied. Please replace it and try again.

I don't see how that is possible. The source of the page indicates that the modification hasn't been applied.
Could you provide a FTP access so that we can directly check the code ?

I don't know why but there is something triming the return lines on your website apparently.
I've changed the lines:
$doc->addScriptDeclaration("<!--\n".$js."\n//-->");

to:
$doc->addScriptDeclaration("\n".$js."\n");

and that has solved the problem.

That one won't be as it's not a fix.
Using "<!--\n".$js."\n//-->" is not a problem and in fact the recommended way of adding javascript in joomla in order to have a HTML valid page. If we had that last modification, it wouldn't be HTML valid and we would have complains about that.
Also, that works for everyone else. There is really something on your website messing with the javascript somewhere.

So make sure that you back up these two files on even better, that you redo these changes in the new version of these files if you still have the problem when you update.
The cart.php file should change much in the future. However, the other one will.