Nintendo may be able to replace it only if it's still under warranty. But if not, you're better off contacting your home insurance (if you have it that is) and getting it replaced that way. If you don't have it insured... then you could try buying a new cord and see if it's just that.
I've had that happened in the past and we honestly thought the entire system was fried. But a year or so later, when we realized that the insurance company was not going to pick up the stuff they were supposed to get, I tested the system out by plugging the old system into the new AC power cord and it worked. Turned out, it just fried the cord- not the entire system. But I can't guarantee that will work the same with your issue though.
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