Alienware m17x r3 motherboard dead/dying???

Hi,
So, my m17x r3 has had the following issues.

First of all a stick of ram failed on me:
- When I ran ePSA diagnostics I was presented with the following error code 2000-0123.
- So, I identified the stick and removed it.

Secondly all of a sudden my laptop black screened:
- After a panicky few hours I discovered it was related to my amd 6970m graphics card.
- ePSA threw up the following error code 2000-0332.
- So, I googled the hell out of the code and tried every thing I could find, from re-flashing the bios, reinstalling my drivers, fresh install of windows, you name it I've tried it.

So am I safe to say my graphics card is dead??

My concern is that the issues above my be related to a failing mother board? Two components failing in the space of two months. How do I verify my mother board is ok??

If my mother board is in good health I think I'll get some new RAM and GPU but for now I'm stuck.

My laptop is currently running on only 4gbs of ram and is using the integrated Intel HD3000 graphics card. Not too happy after spending €3000.

Any advice or recommendations greatly appreciated.

Also:
My laptop has the hm67 express chipset, so is it common for the motherboard to fail?

I came across this: http://news.techworld.com/sme/3266841/dell-offers-free-motherboard-replacement-for-faulty-sandy-bridge-chipsets/

I ordered my laptop on the 15th of march 2011.