Are you sure it is dead (high resistance across it) and not a bad solder joint or something upstream or downstream from it? I rarely see such LEDs go pop (they are usually run at way too low of a current to do that) but rare is not impossible and we are many years on. Simple enough test though if you just shove a normal through hole LED across it and see if it glows, or use a multimeter to see if it is getting voltage (don't like measuring resistance of things in circuit, can desolder or lift a leg I guess, or if you have a reference example on another board...) or maybe the diode check of the multimeter to see if it glows when the meter is providing the voltage.
LEDs are usually fairly boring and basic. Some of the multicoloured ones can get harder, and they appeared in a few things around the time the GBA was new, but I don't think that is the case here (should just be a plain colour, for multicoloured they tend to have more than two legs). Have seen a few people shove random colours in there before as well (see some case mods). To that end it is probably more a token check to see it will handle the voltage (or adapting a voltage) and finding one in a suitable size and shape. Most electronics vendors will have thousands of the things in all shapes, sizes, colours and whatever else for you to pick from.