I just had a similar problem this morning trying to install a game to my hard drive. Plugging it in again after the DLC has been checked offline and reconnecting while still in-game via the guide should let you get into a multiplayer match, if you want. If a game, especially an EA game gets stuck on that download screen, it's because a server isn't responding properly. based on your behavior with this, you should have chucked your computer out of a window by now. I'm surprised you still manage to have a computer to type on when so much worse can happen on that. That's your issue here, not the system or the games. It should turn you off of day one purchases, since that's when the problems arise. It should turn you off to listening to them blindly. So the thing is, a lot of times support people are idiots, reading off of a script. You know I did my part, bought it all day 1, paid full price, and it's been a pretty shitty experience all around. I called and cancelled my xboxlive membership and I threw my xbox Mass Effect copies into a box in the basement. The whole experience has really turned me off to XBox online gaming and DLC. It's a more widespread problem than I imagined but no one is getting much of a response from EA/Bioware on it other than they are collecting user data and looking into it. The word over on the bioware forum is that this bug won't be addressed until the next round of DLC, at best.

Mass effect 3 crash on multiplayer