This issue stems from four main sources: connection issues, security software, background applications and third-party anti-cheat applications. If your computer is behind a router with a firewall, you must open the ports that Steam uses to connect to the Internet.

If you get the unable to establish connection error in CS2 then the first thing you have to do is to ensure there's nothing wrong with your internet. If that isn't the cause, then restart CS2, verify game files, and disable any background applications you might have enabled.