At first i got the same Problem even HL2:Deathmatch was frozen when i tried to get Server-Info.
Be sure you've allowed the Program hl2.exe to access the Internet (Firewall).
Changing the Firewall settings to something like Gamemode (if this is available in your FW), might be also helpfull.
First installing the SDK-Base, then HL2:DM and then GE:S could be a smart idea.