Could be multiple causes but most common includes drop damage, water damage, or internal issues. Mot of the time a screen repair will fix the issue unless there is something else wrong with the phone. But I would start at a screen fix!

Seems like your Gameboy has had some water damage in the past, from your photos that looks like rusty screws. In that case you will need to replace the screen as it may have died of water damage or just old age. Make sure the connectors on the board are not damaged too. Good news it it seems to have power if you are able to turn it on and it makes sounds. So I think it is salvageable just needs some upgrades to put it back into working condition.