Alienware m17x R3 blank screen 8 beeps Nvidia GTX 560M problem

Here's the problem with my Alienware m17x R3 (also see accompanying pictures):

1. The laptop went dead while in use. The screen went black first, but the sound was still working.

2. Now, it shows a black screen when powered on and then starts giving 8 beeps, which repeats in a cycle.

3. Tried the following steps, but they did not change the symptoms:

a. Replaced the CMOS battery with a new one.
b. Connecting an external monitor and pressing Fn-F6 for toggle internal LED / external monitor – no image on the external monitor but video signal seems to be detected (the external monitor tries to adjust resolution momentarily).
c. Removed the NVIDIA GTX 560M graphics card and inspected it – the white foam below the card shows a brown burn mark (see photo), the corresponding chip on the card also seems to be burnt (see photo). Removing the graphics card along with its heat sink and fan and connecting an external monitor to try using the integrated graphics also seems to show no image on the external monitor, although video signal seems to be detected (the external monitor tries to adjust resolution momentarily).
d. Blind flash of BIOS with A12 BIOS from Alienware website.

Suggestions would be appreciated.