Yep, definitely sounds like a battery issue to me, unfortunately if it doesn't do it on power then that is the most likely option. As lithium batteries age, their internal resistance rises and therefore the current that they can safely output falls. If the laptop is demanding more power than the battery can handle, then it will shut off until you plug it back in. It likely tripped a over-discharge circuit in the battery hence why it refused to boot until you plugged it into power again. Hope this helps!