I take it you're running a game through a normal listen server (eg creating a game from main menu) and not a dedicated one, correct?
Also, does your computer access internet through a router or is it directly connected to the internet?
If it is behind a router, your router's firewall is blocking communications through the ports necessary for a server to gain access to the outside world. So even though Steam Friends shows you as being in game and in a server, the game server is prohibited from gaining access to the steam server list, and more importantly your brother's computer, ie the "Server is not responding" spiel. The game's address should also read as a subnet address and not a normal IP address.
What you are going to have to do is set up Port Forwarding on your router. In order to do that you are going to have to first gain access to the router. I can only comment on how to do this for a Linksys router, so hopefully you know how to do that. Its typically done through a web browser by typing its address (typically the first address in your subnet, eg 192.168.1.1 for Linksys). Enter the username and password if you are prompted for it.
Right here is where I'm going to stop and confirm what type of router you are using.
In the mean time you can have a look at
this page, it will aide you in setting up port forwarding for pretty much any router, and quite a few specific games. Select your specific router, skip the advertisement and when you browse through the applications section you want to find "Half-Life 2 Steam Server". Follow the directions there. It may take some time tinkering but you should be able to get it eventually. If you need further help just reply here.
I should also take time to mention that this is inherently dangerous as it is in fact semi-permanently opening ports on your router that will be open, and stay open so long as you have those ports enabled to be forwarded.