It seems that the problem with my computer is the PSU, rather than the hard disk. I say this because the 8-gig stand-in hard disk started doing the same thing as the old hard disk. This happened the morning after I installed Ubuntu on it. The CD-ROM then started repeatedly making the noise it makes on start-up. Careful listening to the hard disk revealed that it was repeatedly spinning up and down. This made me think that perhaps the PSU was doing something weird and cutting off power to the disks repetitively.
A couple of days later I managed to borrow a PSU off a friend. Pop in the borrowed PSU; the PC has been up a couple of days now, so it looks like the PSU may indeed have been to blame. I’m going to keep the borrowed PSU and do some emerging, power-cycling and so on to ensure that things survive. If they do then it is time to order a new PSU, I guess.