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So, I bought CE and installed and authenticated/verified it on computer A. I disconnected computer A from the internet, connected computer B to the internet (which does not have a DVD drive) and downloaded Steam and HL2 from my preexisting account. Now, when I try to play the preloaded HL2 on computer B, it says
No Disc Inserted
There must be some way to play the game without the DVD for those who downloaded the game, since Valve designed the Steam system to allow people to download the game and play without the DVD.