My first thought was that it was a loose connection between the graphics card and the monitor, but no.
Driver issue? No.
Then because the PC was still partly open after swapping some hard drives around, I touched the graphics card.
It was running hot. A quick feel revealed that its fan had failed. Close everything down and switch it off.
- new card fan (there's a Maplin near by, should be cheap, could be difficult to fit, might have damaged the card already), or
- get one of those 'fans in a PCI slot' and put it next to the graphics card (a bit more expensive? Loses a slot and I don't have any spare. Memo to self: even though motherboards now have more on, four slots, including one for the graphics card, is unlikely to be enough if you want extra goodies), or
- new graphics card (most expensive, Maplin is not the best place to get one, this one is fast enough for what I want at the moment - i.e. Half-Life 1, not 2 - and the future's PCI Express not AGP).
I'd more or less settled on getting a PCI slot one, but Maplin turned out to have a replacement heatsink and fan for the card (clearly this was part of the Nvidia spec to makers) for the same price. Copper rather than aluminium, and not as high (the original one was at the edge of the AGP spec in how much space it took up.)
And now it's running very cool. So cool I'm tempted to overclock it in fact.
I'm quite glad I hadn't got around to installing games on that PC yet, especially the 'lets see how many 3D graphics we can whiz around' sort, because that really would have pushed the temperature up...