Well, I ran MemTest86+ and it passed with no errors. I was able to run an MPrime test for a couple of hours without any problems - so I guess the base system is stable.
@Grevane: I just looked at Asus' forums and now I feel sick. I'm shocked that such a nice looking motherboard with such an excellent feature set could turn out to be a lemon for that many people.
Oh - there's another thing I'm having trouble with, related to the motherboard and memory. No matter what I do, the motherboard refuses to run my PC2-9200 1150MHz rated memory at its full speed. The very max I can go is about 970MHz. Any more and I can't POST at all. I've been through every setting in the BIOS, copied other peoples' templates from the memory manufacturer's site, tweaked voltages and lots and lots of settings. This motherboard just won't let my memory run near its rated speed at all!
What I'm worried about is that if I RMA my graphics card alone, it might be tested to be working fine, and if I RMA my motherboard, it might be tested to be working fine. Given what people seem to be writing, I think that the motherboard might still be partly to blame; something to do with its chipset that doesn't show up when using the computer for simple desktop needs. My gut feeling tells me that it might be this combination of hardware.
I am spending ~£2000 on finance with Scan and I really, really hope that they can make me happy here. Would I be able to return both motherboard and graphics card so that they could be tested together?