My little boy put a little too much weight on the front of my Wii, where the disc loads. There was a disc in the system and as it turns out, the loading mechanism loads the disc and then places two rather flimsy metal tabs in front of the slot to prevent you from trying to load any other games.
What I found was that I could load Gamecube discs just fine, but Wii discs wouldn't load because the tabs that are meant to prevent you from loading another disc were preventing the Wii disc from spinning/loading. I would get a message to remove the disc, turn of the Wii and consult the manual.
I can't find an image of the front of the disc mechanism, as a photo would really help clear this up. At any rate, if you load a disc and then use your finger to slightly pry open the slot and move the felt away, you'll see two bare metal tabs. These tabs seem to be pretty flimsy and are easily bent. I used a flat head screwdriver to pull the tabs away from the inside of the Wii while a gamecube disc was loaded, now my Wii discs work again.