Did you try inserting a few more games than just the one you're inserting when the problem occurs? The disc you're trying to play may either be scratched or dusty.
Nintendo will pretty much tell you the SAME thing.
Did you do something to your Wii (eg, mod chip?) If not, is it covered by warranty? If so, Nintendo may be able to fix it for free! Or if not for a price... Lol, basically I'm saying either call Nintendo or go to support.nintendo.com