Had a few more, but think I may have found the cause. I decided to move an old soundcard (old, but in my opinion still better than the built in AC97) to this machine and realised that the graphics card was very loosely seated. My case had a proprietary retaining system instead of old-fashioned screws, and it couldn't cope with a double slot graphics card, so I'd just left the card hand-slotted.
Since then I've changed the graphics card and whilst it's still double slot the retaining system seems to work around it. I'm hoping that's an end to my problems!