You need to have your copy of Half-Life activated on Steam.
Download/Install Steam if you haven't done so already, then click on "Add game using CD Key" on the bottom left of the main window. After that just follow the procedure and you should be fine. You might have to validate again though.
Also, ESF 1.3 Open Beta was just a test version of the game meant to check for bugs and stuff. It is nowhere near stable and thus not meant for normal play. Stick with 1.2.3 for now until Final gets released.