I'm not sure about your specific problem, but I called Nintendo when my Wii quit playing any and all discs. I got a friendly, helpful guy who sent me a mailer whereby I sent them my Wii (after removing the SD card and any disc I had in it), and they sent it back and restarted my warranty date. I did have to pay for packaging, but not the shipping cost. (I'm a wuss and had UPS Store pack it.)
Granted, I had no Wii for 10 days or so, but I was delighted overall, given similar experiences I've had with computers with fried motherboards and such.
I'd call them and see what they have to say. Odds are they are used to dealing with your problem and have a plan at the ready.