Aluminum Unibody Macbook battery chipset problem

I have a 2 GHz Aluminum Unibody Macbook which is a little under the weather these days. Randomly, at any amount of charge, the computer with shut off as though it has ran out of battery. Once plugged into the wall it will come back alive and re-load everything back in the RAM the same way it normally would if you ran out of battery. The problem is that the battery actually still has a charge. After being on for a few minutes it will (usually) see that the battery has a charge and will be ok without the wall plug again. When it "dies" both the leds reporting the battery charge and the menu will show %0, and iStat Pro will show very low health. However, again, once the OS see's that everything it ok, iStat Pro will report good health.

So far, I've reset the SMC RAM and the PRAM with no luck. I'm about to reinstall the OS as a last resort although I'm pretty sure that's not the problem. To my understanding the battery chipset is located in the machine, not in the battery, so replacing the battery doesn't make a lot of sense to me (seeing as it is actually holding charge).

Ideas? Anyone? I'm at a loss here...

Mat