Possible Solution - But Not on Steam
Out of desperation, and taking advantage of another half price offer, I bought the Complete AOE3, but this time through GAMESTOP. After downloading the game, I tried to start it up, but received the message that I had to install MSXML 4.0. This I did,and the game WORKED. Thinking that this would also solve the Steam problem, I tried to play TAD, but game the same "couldn't load the map" error.
I think that the problem may be on Steam's end - they are not sending all the components of the game in the download. I have tried uninstalling, redownloading (which is necessitated by the uninstall) the files, and reinstalling, multiple times. There must be something wrong on Steam's end. Gamestop seems to work fine.