The battery on my Sony walkman NWA3000s doesnt hold a charge. ?

For the most part my walkman sat in a cradle being used as necessary. However, now when i take it off to listen through my earphones, the battery drops to no charge in a bot 5 minutes. When it goes back on the cradle to charge, it charges up again so the battery is draining? Can it be fixed and if so how much? I'm aware that it is an old model but would like to hang on to it as it's a 20GB model.

Brian.
April 2010