PSP-1000 (Japanese) running OFW 6.37

Every now and again, the battery indicator keeps disappearing and then reappearing a second later. This happens continually until I shutdown and restart (complete shutdown - sending it to sleep and bringing it back does not work). There have been a couple of instances where the power has just completely dissapeared from my console. And there has been one instance where I've tried to start up my psp and it wouldn't, no green light or anything, until I connected it to mains supply and then it started up ok.

I'm guessing a battery problem. I haven't been able to try another battery (I guess I should have done that first before posting. I'll buy one next pay day), but could it also be a power unit problem?

Any help greatly appreciated