The quality of your soldering looks okay, but there's too much wire exposed at the contact points; it looks like you kept the iron on there a little too long and the coating on the wire melted off. It probably works fine when the gameboy is disassembled but when you close it it may be pressing the wire against some other contact and introducing a constant voltage into the signal which you're hearing as hum.
Basically you need to undo the solder joints, cut the exposed part of the wire down shorter, and redo the solder joints faster - it might help to apply the iron to the contact on the board, then as soon as the solder flows, apply the wire, then remove the iron. This should all take no more than a second or two for each joint, all told. You might find some junk electronics to practice on first before attempting this again!
Good luck!