If the two computers are not on the same subnet (either wireless or wired), that does complicate matters. The server will either need a static IP address or you will have to set up port forwarding on the router controlling the server's subnet to pass incoming connections to the external_ip:port to that specific computer. (At least, that's my understanding -- I don't claim to be an expert on networking.)
(The port doesn't indicate which computer to connect to, it is more of a connector to a specific application on the computer at the given IP address.)
For simplicity, you should get this working with two computers on the same network subnet (or using a server with a static IP).
One thing to check is whether the server is actually listening for remote connections. You can use the command line netstat
utility.
Run:
netstat -a
In the long list it prints out, you should find:
tcp4 0 0 localhost.6437 *.* LISTEN
That shows (on my computer), that the service is ONLY listening on localhost. You should see *.6437
instead on your server.