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Sounds like you may have a flaky laser in your Xbox that may not be quite as strong as it should be. Or they just didn't print that disc as well as they should have. Bad production methods, maybe. Even if the disc is readable in another machine, it may be marginal.
I got it for PC, and their quality control in general was terrible on it (absolutely refused to work right on my system, and mine exceeded recommendations). Note that if you haven't played FFXI before, don't get your hopes up. I personally found it to be sub-par in terms of quality and after fighting to get it work (and briefly getting the graphics to show uncorrupted for about 5 minutes) for several hours, I canceled my account, uninstalled it, and trashed it.
Yeah, and I recommend you try to get one from a different batch, if at all possible. If you don't already like FFXI, though, my advice would be to pass on this game. It's really, really bad. Even a lot of Final Fantasy lovers agree with that.
It's probably a combination. Chances are your new Xbox's laser isn't quite as strong as most others. Everything else may work just fine, or not. But it doesn't at all surprise me that the FFXI disc would give you trouble. As old as that game is, they're not exactly paying for premium production. See if you can get a better disc.