I have the same problem my SP2 doesn't want to turn on I forget to use it for about 20 days and now he is on mood sleep of death don't want to turn on and the charger connector light flashes constantly. The battery does not charge.
Then Try the steps for reset. Hold power button 30 sec. Hold power + volume up for 30 sec. Release all buttons. Wait 10 sec. Press power. Nothing. Black screen only. The surface won't start. Then simply hold the power button for 2 minutes. Then released and hold for 3 minutes. Released and press power. Nothing. Black screen only. The surface won't start. Then Try that steps. Press and hold the volume-down button on Surface. While holding down the volume-down button, press and release the power button. Again surface won't start. Attached keyboard try again. Detached keyboard and try again. Insert power supply... Nothing. Dead surface. What to do?