Error: 10061 whenever I change the connection port from default

[Casey Diercks]

I have VNC set up on two computers on the same network.  One is a Windows
2000 machine, and the other is an XP Pro machine.  When I install VNC on
both and use them with their default settings everything works fine.  The
problem is that I want to be able to access both from outside the network,
so I have to change the incoming connection port on at least one of them.
But whenever I change either of the ports in the Connections tab, the server
will no longer accept incoming connections.  I get error Connection Refused:
10061.  What's going on here?  I read on the FAQs that you can change either
of the ports to suit your needs.  I have my router set to forward incoming
connections between ports 5600 to 5700 to machine one, and between ports
5800 to 5900 to machine two.  I haven't changed any other settings from
their default.