WuTangTurtle and I were in the same boat. I got some error # (not the one you got) + "There is a problem with the WiiConnect24 service. Try again later." After reading about it online and calling Nintendo, it was confirmed: I had a bricked Wii. With Advance Replacement, they got a new Wii in my hands before I had to send in the old one. It's the way to go unless you have saved data you can't afford to lose. In that case, they'll have to repair your actual unit, meaning you'll have to go Wii-less for a week or two.
Now, is your Wii bricked? I don't know, but I'd worry just a little if I were you. Call Nintendo, see what they say.