Steam – Specific server not responding specifically for me

If it's only people on the same LAN that can connect, then the problem is almost definitely to do with the server's firewall or, more likely, the router that your friend is using.

In the first case, it may be that the firewall is configured to accept connections from computers on the same subnet (i.e. on the LAN), but block connections coming from computers outside the subnet. Set the firewall permissions on the server, and you're set.

In the second case, it's likely that the ports used by the server aren't being forwarded by the router. The router doesn't know what to do with incoming connections that weren't initiated by one of the computers on the LAN, and the TF2 server might not be smart enough to tell the router that it's listening on port 270xx. Forward the required ports using the router (web) configuration tool, and you should be good to go.

Here is some more information about setting up a server, and the needed ports.

EDIT: @Matthew Read posted a nice answer on a similar question listing the ports in use by Valve games.

Based on complaints on the steam community forum the game is currently broken for a number of people.

However, the asker was able to solve the problem by downloading a .dll file here. Apparently steam is not downloading .dlls appropriately on some x64 systems