Source: HalfLife2.net

A lot of students in America and other colleges in the world are unable to play our beloved game. This is because many collage networks have certain ports blocked to prevent viruses from getting in, and other things from happening. Most of the time it's of course a good thing, but sadly Steam also needs those ports to authenticate Half-Life 2:

Many Colleges, Universities, Schools and Large Corporations are now actively blocking ports to prevent virus, trojan and Internet worm problems as well as to prevent misuse of their networks.
If you are having problems and you are on one of these complex networks that are intentionally blocking ports required for Steam to work then you may not be able to connect to Steam and play.

The authentication is a great thing for stopping warez using persons but sadly it's also giving problems for others that have bought the game. Time will tell if a solution is going to be given. For more info check the site of Steam.