Remove the AC, the battery and then press and hold the power button for say 20 seconds. Release the button, put the battery in, connect the AC and give it a minute. Try the power button.
I had a Dell D600 for almost three years now, and a few hours ago I left to go out for a bit and I unplugged my laptop from the wall-outlet power adpater and put it to sleep. When I got back home the laptop would not wake up out of hibernation mode, so I held down the power button and shut it off. Happens occasionally.
When I tried to turn it on when it was just on battery power, all of the indicator lights flickered and the computer hummed for three seconds before shutting off; all of the indicator lights shut off unless I pressed the power button, even though the laptop was at full power.
When I plugged my laptop back into the wall outlet, the power indicator light did not turn on, and when I tried to boot the machine I achieved the same end result: flickering of lights then nothing.