Bought some fancy new IDE & floppy cables to install in nessus, on the theory that the old ones were failing. Alas, the new cables were just too big to plug both into the motherboard at the same time.
I suppose I'll have to return them.
But when I opened up the case, I discovered that nessus was full of dust. I used up pretty much an entire can of air cleaning it out. I imagine that's the real cause of nessus' recent problems.
While I had the case open, I removed the DVD decoder card. (A RealMagic Hollywood Plus, or some such.) It never did work very well, and I haven't used it in years.
One little oopsie: I changed the DVD-ROM drive from master to slave on the second IDE chain (the CD burner went the other way). This caused Windows to think they were entirely new devices, so they got new drive letters, D: and E:. This pushed the second hard disk from D: to F:, which was rather annoying. But a few minutes in Disk Manager and all was as it had been.
I think I'll leave nessus running overnight (both disks are seriously fragmented and in need of tidying-up); if it's still sane come morning, I will declare it cured.