So there is also problem with permissions, but this is not related to fcgi setup I think..
The permissions are fine for fastcgi, you get the permission problem only because you use mod_php, so the permission problm does not exist on fastcgi setups. What you can do as temporary workaround si to run:
chown 660 /usr/local/ispconfig/interface/lib/config.inc.php
to use mod_php.