A simple way to drastically reduce the hum on a GBA:
After pointing them with some sandpaper first, just poke the capacitor's wires into the holes, no soldering required.
The capacitor has to be in this exact position, otherwise it won't fit into the case. Of course legs should not touch any other wires/parts, it may be a good idea to insulate them somehow. At least + should be shorter than shown here and not get so close to C36 on the board.
This is an early board version (AGB-CPU-03), on later revisions, the same mod is possible, but the layout is different.