1. Make sure that Steam and HL2 are completely updated.
2. While still connected to the internet start HL2
3. Play around a bit. Save a game. Exit.
4. Disconnect your internet.
5. Restart PC.
6. When Steam asks, tell it to run in offline mode.
7. Run HL2
This worked for me. Let me know if it works for you.
I noticed with mine that it did take a few days to be avalible off line even after had all updates
. It tells you when it avalible off line when you click on the steam icon in the system tray.
Not at home so cant guide you there so that you can check status.