I\'d talk to Nintendo before you do anything, see what they have to say about it and maybe they can help you fix it. There is a 12 month warranty on the GC itself. If you are past the warranty then perhaps you can talk them into replacing your GC. I know they have a 1-800 number so you have nothing to lose.
If you do decide to do it yourself then you should know it could be any one of several problems. Best case scenario is that you simply need to clean the laser or recalibrate it, worst case scenario is that you might need to replace the laser.
Read this
link.
Anyway, here is a guide I found...
$11.95 to download...
http://www.ps2repairguides.com/Gamecube.htmThat\'s all I could find but I\'m willing to bet there is a free one somewhere.
I\'ve only had to take apart my Xbox to put in a new dvd drive but I\'ll tell you it was very simple, it might have taken a little over 5 minutes. I can\'t imagine the GC being tough to take apart, though you might need some special tools which could cost you upwards of $20. Not to mention the laser, if you need one, will cost about $20-30. You might be able to find a second hand gc cheaper than it would be to fix your old one.
You have options, I\'d open it up as a last resort.