This happened to me once and I contacted Steam support and they told me to delete the L4D2 files that were in my SteamApps folder and then I was able to play it without the "Steam servers too busy at this moment" error message.
wait for it to be not busy .-.like in a couple days
I have deleted everything in common except for:left4dead2left4dead2_dlc1left4dead2_dlc2left4dead2_dlc3Still not working.
Reinstall as in redownload it? Or something else?