There is one difference between site A and B and that is that I have not yet recieved the domain for site B. I solved this by creating a symlink from the sharedip directory (where I ended up when I typed in the ip-address to the server in my browser) to the web-directory of site B. So now when I type in xxx.xxx.x.xx/symlink/ I come to the default index.html file of site B and when I type in xxx.xxx.x.xx/symlink/index.php I come to the joomla index.php file, but like I said, it just comes up on the screen as plain text.
and that exactly your problem. You can not access websites trogh a symlink from the shared IP directory. >ou have to access the site trogh its domain name, if the domain has not been registered yet, then add it to the hosts file on your workstation to be able to use it to access the site.