The Gameboy I had was in fairly good condition, with the exception of several vertical lines through the display. After some research, I learned this is usually due to a faulty display connector, where the solder connections have weakened and eventually separated from the top layer of the display circuitry. Using a soldering iron, I learned that we can reflow (that is, remelt and reconnect) this broken solder below the connector. It’s not that hard, and fixes what is perhaps the most common issue with these Gameboys.
Step 1: Taking It Apart
Once you take those screws out, don’t pull the Gameboy apart quickly. There’s a fairly short ribbon connector connecting the screen half of the Gameboy to the circuitry half. Carefully hinge unit so the screen half is face down on your desk with the circuitry portion sticking vertically upward. You could disconnect the ribbon cable at this point (it’s a ZIF socket, so the connector just slides out), but I didn’t want to bother having to reconnect it when I was done. You can do this repair quite easily without having to put this connector back in.