Well, I didn't notice the date your post was until I clicked the quote button.... but anyway, I always recommend cleaning the leads on both the battery and on the PSP from time to time... Do scrub it, obviously, but a light rubbing from a q-tip would do it wonders.

Granted, I can't say this was your problem, but I like to offer suggestions to not make you spend more money than you have to. If it doesn't work, at least you know it wasn't that.