I've seen this problem a few times, and it's almost always something to do with the Wii console itself. I would contact Nintendo by phone or e-mail (phone is the better option in my experience) about the issue. Nintendo System Set-Up, Troubleshooting and Repair:, the first number, is the one you want. Although, Nintendo reps shouldn't be on the phone at this time, so you'll have to wait until tomorrow. Sorry. =(
If the Nintendo reps can't help you fix it and you have the warranty, you should either be able to have your Wii repaired, or replaced. So as long as you have that warranty, even if it's a week or two, you should have a working Wii. Hope this helps.