From what I've read, this is a known issue with the 360S consoles. I can't say with any certainty (I'm well read, but not psychic, LOL) but I've seen it posted in Xbox-related places that it is something they are working on a patch for.
I also took note that there was a flurry of posts not long ago from folks who had purchased DAI on disc for the Xbox 360 and when they got it they were unable to install and run it -- the game would bomb out during install, or would simply never give the option to finish installing after disc 1.
The common thread there appears to be that they all purchased the game from Amazon.com and it looks to have been a bad batch of discs. Unfortunately, no mention of if or how that was resolved.
Don't know if that helps you or not, but I figured a little information is better to have than no apparent response. :cathappy: