My Dell XPS 17 L702X just stopped working and now won't boot.

I was using my Dell XPS 17 L702X last night and it suddenly switched itself off with no warning.  I pressed the power button to reboot it but it won't restart.  When the power button is pressed, it lights up, sounds like the HDDs spin up, the row of LEDs on the control strip to the right of the power button light up in sequence, then all go off and it shuts down (all within about 3 seconds).  No sign of life on the screen at all.  I've tried numerous times, both on battery and on mains (including mains with the battery removed). The battery is fully charged (all LEDs light when pressing the test button).

I've removed each of the RAM cards, both in turn and together and even swapped them over.  With all RAM removed, I get the usual two beep code.  Likewise, I've removed/swapped the two HDDs.  I've tested the HDDs on another PC and both are fine.

I've stripped the laptop down to motherboard level, checked connections, removed/tested/replaced the BIOS battery and even re-seated the processor and cleaned the fan, etc.  There's no obvious signs of component damage.

Has anyone else encountered this problem and, if so, any ideas on what the problem might be?

Mike