SFC3 is still played online quite regularly. There are about one or two servers online almost all the time open for the general public, and a few sometimes hosted for beta testing mods or for personal fleet/clan use. The major mods, such as Unity, NDF, Island Wars, GAW, Sedition, Final Frontier, are open to all people, but most require you to register for the campaign in order to get the password for the server.
http://sfc3.puterz.net/ This is the website where you can get the most up to date information for most of the major SFC3 mods currently playing right now.
If you are having problems connecting to the SFC3 Access Servers, you will have to make adjustments to your router, if you have one, and also probably disable any firewalls you have, or grant full access to SFC3 in your firewall settings, but sometimes your connection is still wonky if you have your firewall on.
Normally, when I get ready to fly a new campaign, I delete my old install and install the mod over a fresh install of the game, and I have to let the game try and connect to the access servers a couple times before it finally finds my IP. If you haven't tried, just let the game attempt to connect and if/when it comes up with a box saying to input your IP addy, just shut down the game, restart, and connect to the D3 again. For me this usually works like a charm.
About router settings, I can't help you there, but I know many D2 and D3 pilots fly online while using a router, and router settings for both D2 and D3 are pretty much the same. Just post for help in these forums.