Unfortunately, sometimes a computer with a totally dead battery won't start up even when it's plugged into the wall. But it will start working again if you replace the battery. This just happened to an old laptop of mine, don't ask me why.
I think it's related to the power management systems that provide power to the PRAM; that power still has to pass through the battery even if it's plugged into the wall. I'm not sure about that; it's just a guess.
