It's been more than 6 months that my Wii was producing an awful lawn mower sound in the disk drive, and I finally decided to open it up and "try" to fix the problem.
Since I've seen other people with similar problems on YouTube, such as:
I decided to put my experience on how I fixed it.
You will need Nintendo screwdriver, which you can easily find on eBay.
I've used the following video as a guide during the disassembling of my console:
There is one screw above your Wii's drive that is right above the power button, loose it a little and stick something to level the plate a little bit up. You can test this with your Wii still opened until you don't hear that noise anymore.
Here is a front picture of my fixed Wii (Flickr notes):
I should have taken a picture from above, but I was too happy that the problem was gone, that I just remember to register how I did it after most of my Wii had been put back together already.
Hope it helps someone!