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:

Now how I did it:

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 (follow the link to see the 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!