When I enter the Game I get a prompt from "Games for Windows" LiveID asking for my e-mail address and password. I am a registered user on the Games for Windows Account Support and can sign in there. BUT when I try to sign in at the Prompt at the enter Game Window it continually gives me a message that either my Email address or my Password is incorrect. This is NOT the case! I enter them correctly but the game does not accept it. Thus I cannot play the game. I even went so far as to change my Password out to see if that would solve the problem. The Game support site accepted my change, but AGAIN when I went to log into the Game the Game entrance prompt would not accept my information. Any suggestions?

I'm pretty sure a windows live id is something completely different from Games for Windows Account Support. You need to create a new Windows Live Account. Microsoft (and steam as well) have one account for the game and another for support. This is a security feature (If your game's account is hijacked, you can still report it with the other account).

In any case, you can run Fallout 3 without logging in to GFWL. The only difference is that your saves are in a different folder and you don't get any achievements.