Hey! So I had to clean the contacts on the motherboard fairly vigorously with rubbing alcohol and a microfiber cloth in order to get the buttons to register again. In my case it appears that something sugary had been spilled on the Gameboy and seeped down to the motherboard. I didn't have to replace the buttons, just clean the button membranes of residue.
And the Oxyclean solution I used on the housing was about 1/4 cup liquid concentrated Oxyclean to 32 oz of warm water. I soaked all plastics for 2 hours and then I brushed with a soft bristle toothbrush. It won't damage the color of your plastics at all, but may lighten them to the degree that you can see in my pics. Lots of people use the Oxyclean solution for colored Gameboys. There are suggestions out there for stronger solution recipes but I didn't want to take any risks. More than anything, it seems like Oxyclean helps with the yellowing that occurs over time, but beyond that, the soak helps make the grime loosen up so it can be brushed out of the crevasses.
Edit: you will need a precision screwdriver set that includes triwing bits to disassemble the Gameboy. I got a budget set on Amazon by a company called "Jorest" for $9 USD. It included all the right bits and spudgers and picks to get it cleaned up no problem. I'm not sure if links to products are allowed here so I'm not comfortable providing a direct link. Part number was AJJOJM0101ORDCAR1 if that helps.