Years ago there was a "virus" floating around, one I assume written by a punk to prank his friends. It was a vbs script that would set the registry flag for "shutdown" battery level in XP to 90-95%, causing windows to shut down almost immediately when it went to battery power.
I haven't seen it in a very long time, but it is easy enough to check. Start the laptop on AC power and enter the BIOS setup, then unplug power and see if it shuts down. That would test actual juice coming from the battery to the motherboard, rather than any sensors or meters that trigger events. It would also help you rule out any other sort of windows corruption being at fault.
But I agree with the others, I think its just a bad battery.
I don't have the laptop with me. The effect when I unplug the AC cord is exactly the same as if I had unplugged the AC cord with no battery in. Normally in windows if the battery reached shutdown level, it goes through a few seconds of entering Sleep or Hibernation or an orderly shutdown of windows and power down - this is different.