The original anon leak beta of HL2 by itself has no set map for the "New Game" button. You have to load all of the maps manually by using the "map (map name)" command in the console. You'll have to download a patch for the button to work. I'm not sure if the button's functionality is restored in the
Mega Patch, but considering the stuff that comes with it, it may be (+Most mods for the beta have the button set).
The button may also work in the
Mega Build when running the original leak, as it is just the beta with the Mega Patch and LeakNet pre-applied + Some mappacks and mods, however it is a bit outdated nowadays, so I'm still not sure. You would probably have to add
XJR9000's fixes for the September 2003 storyline to be 100% sure.
I hope that helped some. I know it may be confusing, but you know, the beta is... well... a beta, so not everyting is in place with the community having to pick up and put back all the pieces in the right place (Or remake them from scratch).