Have you tried installing it on another machine? Also, try cleaning the DVD and the DVD-ROM lens to see if that clears it up.
Also, I can't remember if the game requires you to install with a network connection to verify the game or not. I don't remember that. Is your computer connected to the internet?
Also, some people have ran into problems with the Games for Windows Live aspect of the game. Have you installed the latest Games for Windows Live client? You can download that from Microsoft's web site.
Also, do you have all the latest patches and drivers installed on your machine as well? Otherwise, I would say try installing the game on another machine if you can and see if the same error persists.