I did some more troubleshooting to see if I could zero in on the problem.
I downloaded RivaTuner from the folks at Guru 3D which is a pretty neat tweaking utility generally used by overclockers but I thought it might allow me to selectively disable graphics hardware features like the Pixel\Vertex shaders (yes it does) and possibly help me with memory mapping issues (not sure but probably not). I also downloaded 3D-Mark03 and was going to download 3D-Mark 05 and 06 but as it turns out I didn't need the newer two - 3D Mark03 happily crashes the machine all on its own so there was no point.
I used RivaTuner to step through the process of disabling the two shader types, then locked out anti-aliasing and anisotropic filtering and did a few other minor things that it gave me access to but the end result was always the same. I was partially able to confirm that RivaTuner was doing what it said on the tin as Vista's Aero features got progressively disabled as I turned off the graphic card's higher end DirectX features. It didn't matter though - I still ended up staring at the Black Screen of Death.
So I've accepted now that I have a hardware fault and have raised a ticket with Dell. Lets see how long it takes to get this resolved satisfactorily. The clock is ticking and I keenly await a resolution from Dell.