Alienware Aurora R4 randomly shuts down and won't load the bios for hours

I have a frustrating and bizarre problem with my Alienware Aurora R4.

I've had it about 5 months now and just recently it will either lock up and freeze or power itself off.  Upon powering back on it will go into a cycle of powering on then intermediately off then immediately switching back on.  Sometimes at the point of freezing the Alien FX lights look like its going into sleep mode however I've completely disabled sleep mode on the machine.

However what happens next is very frustrating.  The computer will not load the BIOS at all for several hours.

The computer switches on, the fans and hard disks all spin up but the monitor stays blank and no beeps come from the computer.  The Alienhead logo is not displayed.  I am certain that the monitor is working as expected as I've tried another monitor even another power cable. The only resolution I have is to pull the power cord for 2-3 hours and hope that the next time I start the computer it boots.

When it works it works perfectly fine but this has now become and unacceptable problem.  I use my computer for various things including work and this is getting in the way.

So far after contacting technical support we have changed the GFX card and a support agent has updated all of the drivers (The bios was the latest version).  So far I've spent around about 2.5-3 hours on the phone to tech support.

What can Dell do to resolve this problem?

Thanks

Andy