It was indeed a BIOS related problem (as observantly suggested by lovingboth). I'd had the OK from Tekheads to send the mobo back to be updated, but thanks to this last-minute info I didn't have to after all. The obscure and rather inexplicable trick was to disable Cool 'n' Quiet. This allows an OS to boot, and apparently you can turn it back on again once you've got the up-to-date BIOS.
Now I need to flash the BIOS and then carry on with getting together the less barebonesy bits of the new machine.
lovingboth, I could potentially install Win98SE any time now, as dual boot system setup is supposed to work best when you put the Win on before the Linux. What's the likelihood of your spare copy turning up soon do you think? If you can't find it, my fallback plan is to look for one on eBay, which is fine, but I don't want to do that if you're about to send me one :-)