I guess that the only thing I can do is call Customer Support and get myself a box or sticker or whatever is needed to ship my game console back for repair. Well... at least it is free. A few months later and I would have had to pay for a brand new one.
Update: Hurray, the device is back. In fact, it has been back for almost a week now. And guess what? I got it right on Fallout 3's launch date . In total, the console was away for about ten days (give or take), and all expenses were paid by Microsoft. I even got a Xbox Live Gold membership for a month.