RE: Dell Alienware Alpha Beep Before Shutdown/power off/LED off
I will try to assist you as much as I know as you have to contact Dell support directly.
But as a troubleshooting:
did you double checked the power source?
is the adapter working fine?
Can you try to replace the 2nd end of your adapter (from power socket to adapter 3 pins)
Hope that will help. let me know if any worked.