Like all electronic goods, if it does die - the chances are it will die in its opening 50-100hrs (if not, its likely to last the distance). Its just bad luck - when I got my launch Wii, the SD card reader died the 2nd time I used it.
Its under warranty, go get it replaced. They will get the disc out for you.
Gesta Non Verba
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Wii code: 2263 4706 2910 1099