I've had nothing but trouble with my downloaded version of HL2:E2. After a brief period of running fine it refused to start at all. My only remedy was to reset my machine to a previous restore point. Now, it won't start and gives me a message that the Steam servers are too busy and I should try again in a few minutes. That's been going on for days now. I have logged requests for help with Steam's support group but haven't heard a word from them on any subject. This is the first game I have downloaded from Steam and it will definitely be the last.
Can you open Steam and go to the "my games" tab, is it still there? (I only ask incase you got some international version, as they were all made unusable by Valve because of pricing.)
Whenever I try to launch one of the Source engine games (any HL, counter strike, etc), it makes Steam startup (login etc) can you run it in offline mode? Follow this to use offline mode. Because it says Steam servers busy, in offline mode you do not connect to any steam server.