Sony PSP (PLEASE shops READ DESCRIPTION)

Product Name: Sony PSP (PLEASE shops READ DESCRIPTION)
Sold as-is. Comes with everything pictured: system, protective sleeve, game, and charger. I have no idea what memory stick (if any) is in there. Prongs on wall plug portion of charger are a little bent but I didn't have any shops trouble fitting it into the socket. Only turns on when plugged in so battery might be shot (it doesn't look bloated though as far as I can tell, the curve on top is normal for 1000 models and the bottom is flat). Screen has a fair bit of surface-level scratching but no cracks or missing pixels that I can see. Rest of the outside is in good cosmetic condition but I didn't open it up to look inside. Sound works. System did NOT like booting while i had the game inserted, it whirred very loudly and the screen turned on for a few seconds before the whole system shut back off. Booted quietly without issue once I removed the game. Unfortunately I don't own any other PSP games so I don't know if the issue is the disc itself (it's a little scratched up) or the UMD reader.