Fuck, I have two PSP stocked here, a 2000 with a broken UMD Drive and a launch one that still worked perfectly for ripping my library.
Can a PSP work without the battery, like, by being plugged into the wall or the battery serves as a bridge for power?
Edit: Just checked my launch one, which seems to be OK so far. I did cycle it last year though, but it barely holds charge anymore.
One important thing for you all, do not throw your batteries in the trash bin. Dispose of those responsibly! Look for disposal centers near your postal code.