g4 17 battery/power


So, I have this neat simple g4 17 titanium "colored" machine, now running tiger. Plug in the charger, led stays green, pull the charger out batter goes down to zilch, plug in charger led stays green, powered up or not. When powered up it's calculating charge time forever, machine will run with power adapter. I reset pmu, pram.. no joy. thus.. is the battery itself kaput?

thank you.