About three years ago, I had the same problem. My resolution was simply to buy a new GameCube. It was only after I had purchased a second GameCube that I discovered(on these very forums) the reason why my GameCube was having problems loading the CD's, and how to fix it.
The GameCube's laser gets misaligned over time, and must be recalibrated. In order to do this, you require a Nintendo screw bit(purchasable on eBay) and must take apart your GameCube(carefully). You then twist a screw that is connected to the laser clock-wise(if I remember correctly) just a couple times, and whalla, no more CD errors.
I can't remember the exact details, since my brother was the one who performed the operation. But I happened to take pictures and document the whole process, so if it is really necessay, I'll throw up a quick webpage with all of the details and images.