Rcon Connection Problem

It could be a number of things, and you've already named the first two that come to mind. Both the firewall (if you have one enabled) and your router could be blocking the external connection. Most will allow HTTP, FTP, SMTP, and POP3 traffic to external hosts, but they very often block everything else as a default setting. We'll need a lot more information before we can help. What protocol is your program using? What ports? I see that the RCON class uses UDP; is that enabled in your router? What rules are in your firewall and router? In what order do they appear?

Start by checking your firewall - shut it down temporarily and repeat your test. If that doesn't solve it, move to the router and check the rules installed. You may have to add a rule to allow UDP packets on whatever port you're using at the IP address of the target game server. Remember that you have to enable two rules for each socket - one to allow outbound traffic, and one to receive the response. If disabling the firewall in your computer solved the problem, look at the rules it has implemented, and add rules to allow your controller to work.

Add a bit to your question - I think you're on the right track, but we need more info.