How do I set up a VirtualHost for my mail?

I have two files that are loaded by apache2.conf:

roundcube.conf:

NameVirtualHost *:3333

roundcube.vhost:

<VirtualHost *:3333>

        DocumentRoot /usr/share/roundcube
        DirectoryIndex index.php

        <Directory /usr/share/roundcube>
                Order Allow,Deny
                Allow from all
        </Directory>

</VirtualHost>

I know that both files are loaded and parsed by Apache without errors. When I visit the IP address of my VPS with :3333 I'm getting

Oops! Google Chrome could not connect to 1.2.3.4:3333

I'm getting no errors from Apache or anything, so I suppose that configuration is erroneous. I'm hoping to be able to visit 1.2.3.4:3333 and have /usr/share/roundcube/index.php be opened in my browser.

iptables

root@myservername:~# sudo iptables -L
Chain INPUT (policy ACCEPT)
target     prot opt source               destination
fail2ban-ssh  tcp  --  anywhere             anywhere            multiport dports ssh

Chain FORWARD (policy ACCEPT)
target     prot opt source               destination

Chain OUTPUT (policy ACCEPT)
target     prot opt source               destination

Chain fail2ban-ssh (1 references)
target     prot opt source               destination
RETURN     all  --  anywhere             anywhere

I have added Listen 3333 right below the NameVirtualHost line. It didn't have any effect however. Does order matter when it comes to this? Must for instance NameVirtualHost come before or after <VirtualHost>? Can the same instance of Apache listen to port 80 and 3333 at the same time?

Netstat

root@myservername:/etc/apache2/sites-enabled# netstat -tulpn | grep -e ':3333' -e ':80' -e ':8080' -e ':443'
tcp        0      0 0.0.0.0:3333            0.0.0.0:*               LISTEN      7690/apache2
tcp        0      0 0.0.0.0:8080            0.0.0.0:*               LISTEN      7690/apache2
tcp        0      0 0.0.0.0:80              0.0.0.0:*               LISTEN      7690/apache2
tcp        0      0 0.0.0.0:8081            0.0.0.0:*               LISTEN      7690/apache2
tcp        0      0 0.0.0.0:443             0.0.0.0:*               LISTEN      7690/apache2