OS means Operating System. Like Windows XP, 98 SE, 95, etc.

I'm pretty sure it is not a DNS problem, because you can access websites and everything. I think what is happening is your router is blocking the ports that JJ2 requires, both outgoing and incoming (usually it just blocks incoming).

There is a possibility that the other computer on your network is acting as the router and you don't actually have a real one at all. If this is the case, you need to find out what software it is using and how to configure it. I can't help you with that, so you absolutely need to ask your dad what the network configuration is. We aren't 100% sure that you have a router, but we know that something is blocking the ports you need.

Try disabling the firewall on the other computer, and see what happens. Also try playing JJ2 on that computer. Try the telnet experiment on that computer. If it works, I'm pretty sure that you have a computer acting as a router and not an actual hardware router.