It seems your not alone in this problem I did a little research and it turns out many people have gone through this dilema and have had some luck by contacting Nintendo and having it fixed for free. Read this thread.

Before you go spending money please check this:

Will your Wii read or play GameCube discs?

Borrow a GameCube disc from a pal, or buy a cheap one at a game store or an online auction.

If it works with a GameCube disc then the problem is easy to fix if you like tinkering and have a Triwing screwdriver.

Follow the iFixit guides for taking the Wii apart.

Gently work the mechanical disc loading levers - gently - do not force anything.

Look carefully at the two metal guides which pull the full size disc into the Wii. Both should have white plastic clips about 4 by 3 mm to keep them from scratching the edge of the game disc.

Often one or both of these clips will be missing or broken.

Also the metal guides are sometimes bent outward, almost as if you had forced a disc out and it bent them. Gently bend them back towards the edge of the disc. Put a 5mm piece of heat shrink tubing over each of them if the white plastic clips are broken or missing.

With the cover off, try loading a game disc. If needed, bend the guides so they do NOT touch the disc when it is spinning.

This fixes the problem about 1 time in three in my experience.

The optical drive is a common failure item -- most of them will probably fail after a couple of years of use. If your warranty has expired, you can send it back to Nintendo for replacement or do it yourself -- iFixit has a guide here: Installing Nintendo Wii DVD Drive