There are a few things that might have gone wrong:
1.) You have a Faulty PSP Battery, to tell, turn on your PSP without the battery, just the charger.
2.) You have a CFW ( Custom Firmware ) installed,
a way you can tell is to turn on your PSP while holding the R button
3.) You could have corrosion in your circuits, or a faulty driver.
If you want to repair either of these, send your PSP to the Sony Company with a Proof of Purchase
Dylan, February 2010