My Gameboy advance Sp Charger light is not turning on.

I recently got a gameboy advance sp after many years at a garage sell and the game boy didnt come with a charger. So I played few games on it and when it needed to get charged I went to go buy a charger a KMD one. I plugged the charger to my sp and no charging light is coming on when I plug it to the sp. I still haven't bought a replacement battery because I have read that It could be that the battery is dead but since I havent bought a battery replacement I can't prove that it is the battery that doesn't work. Also the gameboy sp can still turn on but for a few seconds.