I plug in my charger and the charging light flashes on for about a second before it turns off. I'm pretty sure it's not the charger because it works with another GBA SP, though that one is a slightly different model.
The model that isn't working is the newer one, with the brighter screen. I don't know if that has anything to do with the problem. It's also not the battery because it works in my other GBA SP, the older model.