If your GameCube is no longer reading games, it could just need a small boost to the laser power. I’m assuming that you’ve tried swabbing the laser eye with a q-tip and rubbing alcohol already. You’ll need to tear open the system, and rip apart the drive until you are looking at the bottom of the drive control board. To adjust the laser power, you’ll just need a small flathead screwdriver and a multimeter. Do not try to randomly adjust the laser power, you can damage the laser by doing it blindly.
The laser power is controlled by a small potentiometer. It is labeled VR401 on the board. It is highlighted in red in the picture above (click for a larger version). Using the multimeter, check the resistance across the potentiometer. Place one test lead on the leg to the left, and one test lead on the bottom right leg. If it has never been adjusted before, it should read somewhere between 200 and 500 ohms. Note your original reading, because if you end up having to replace the laser, you should set the potentiometer back to the original value first.
Use the screwdriver to drop the value of the pot in 10 or 20 ohm increments. Reassemble as necessary to test between each adjustment. If you put the top case back on, remember to leave the lid open while dropping it on. If you don’t put the top back on, you’ll have to press the sensor switch in the back of the drive manually to fake the lid being closed. If you leave the top off, never look directly at the laser. Depending on your original value, it may take some time to drop it enough to get it reading. It’s better for the longevity of the laser to only adjust it barely enough to successfully read. Do not reduce the value under 120 ohms. Anecdotal evidence suggests you could damage both the laser and the drive control board. Besides, if it doesn’t read by 120 ohms, it is not going to work, so just give up anyway.