Thanks for all the replies.
I'm almost certain it's a failing motherboard. It's certainly related to video playback and is occurring more often now. The boot up isn't always successful and needs two or three attempts; everything locks up again after the XP desktop screen appears. I've decided that the only real cure is to junk the motherboard and processor.
The RAM is DDR2, now outdated. As it is now almost 6 years old, the old XP software needs replacing too. The case is older than the hills and looks very jaded and tatty, the PSU is more recent. I'd need to replace both of those, too.
I priced up the individual components I would like to use and have compared with the prices of ready built "shop package" PCs at my local computer repair shop. They can build me a good spec, complete PC with Windows 7 software (with a few extras thrown in for free) for less than I could buy the equivalent items, for a self-build project.
So, I bit the bullet and got out the credit card. The new PC will be ready for pick up tomorrow.