|Playing Super Mario after repairing the machine.|
We cracked it open and discovered that a chip near the cartridge connector had corrosion completely covering the pins on one side, and a little corrosion on the other. The photo below is after a certain degree of circuit cleaner spray, toothbrush and toothpick work.
The eventual solution was to put it under the USB microscope at highest magnification and clean with an X-Acto hobby knife. This revealed that one of the pins had come completely loose from the circuit board due to the corrosion. Flux was applied with a flux pen, and the contacts re-soldered. We now have a working Gameboy, with Super Mario and Tetris carts!