Assuming each "domain-name.com" is its own Apache virtual host, you should at least start by posting the output of
httpd -S. This will enumerate all the virtual hosts Apache is serving up and indicate the IP:Port combination it is being served on.
If that command does include any namevhost output, several things could be wrong (starting with name-based virtual hosts being disabled in httpd.conf).
If the only output you see is a line stating "default server", it means Apache is only serving up some default content out of /var/www, it sounds like.
If there are multiple lines of output, one namevhost for each domain you are expecting to be served up, you should review your Apache configuration and ensure your Listen and NameVirtualHost statements reference the appropriate IP/Port for your new server. Likewise, in your Apache virtual configurations, ensure that the directives specify the IP address of your new server, not your old one.