Psp will not charge or switch on. no lights. nothing. is there a replacable internal fuse

Since you say it also doesn't turn on when plugged into the charger, it can't be caused by just the battery. It looks like there is anissue with your logic board, but indeed there is a fuse on the logic board that can break. Just google PSP fuse repair and it will show you where to put the bridge. However many times the circuit board actually can be defective and it's not caused by the fuse, so I wouldn't exclude thatpossibility. I work for Sony Repair NYC and we do this repair frequently.

The problem most likely consists in the battery. Purchase a new one.