Not shutting down for 3 days

I am moving this over to the Alienware Club, where other Alienware Owners may have had a similar problem and post what they did to fix the problem.

Reading your post it sounds like the notebook isn't fully turning off. 

1. Unplug the ac adapter from the system
2. Press and hold down the power button for several seconds, until all lights go off on the notebook.
3. Press and the power button again and see if the system boots.

If the lights don't go off, you may want to try removing the battery, 

1. Turn the notebook upside down and remove the door on the bottom of the system. It is held in place by two screws. Remove the screws and then slide the door to the front of the notebook and then lift it off.
2. Once the door is removed you will see the battery.  Gently remove the battery cable,  and unscrew the two securing screws and lift the battery up.
3. Hold the power button down for a few seconds. 
4. Leave the battery out for now, connect the AC adapter and then try powering the notebook back up.

If you continue to have problems you may want to run diagnostics on the system just to make sure that there aren't any hardware defects.  If document will help if you aren't familiar with Alienware diagnostics.

If the diagnostics pass with no errors you may be looking at running recovery on the system.  If you have a recovery key this document will help out.

I hope that this has helped,  please reply back on what you find out and if you where able to get the system up and running again.

TB