At least, Nyx spontaneously bluescreened (a rarity since the Windows 7 upgrade), and on restart refused to load the driver for the graphics card. Looking in the event log the bluescreen was due to the graphics driver repeatedly failing. Device manger shows "Windows has stopped this device because it has reported problems. (Code 43)" for the graphics card, and the consensus online is that this translates as "hardware failure".
The graphical corruption on the BIOS startup screen (rows of blue dots) is something of a hint as well. Last time I saw something like that was with an ATi Rage Pro PCI which objected to being second in the startup order - Nyx only has the one graphics card, so that's unlikely to be an issue this time :)
It'll be quite hard to replace that card. I chose it specifically back when I built Khaos (the predecessor to Nyx) as it was the only decent card on the market with a single-slot cooler, which I needed to be able to use all the PCI slots on the motherboard (itself chosen as I needed 3 PCI slots). Pretty much everything these days has at least a dual-slot cooler on it. Of course, it was only later that I discovered that I'd bought the best possible graphics card (seriously - the 8800GT outperformed just about everything else available, including cards costing an awful lot more). That's true of so much of the build of Nyx - almost everything was bought to fit some odd constraint or other, and most of the parts turned out purely by chance to be very good buys.
Anyway, I'll see if it behaves any better after getting a chance to cool down overnight. There's some suggestion on the internets that this type of failure is thermal-related, and that card has always run a bit hotter than I'd have liked. Certainly whatever thermal gunk nVidia's used on the heatsink looks like it's seen better days.