Thanks for everyone’s comments on the previous post. Independent from all those (very sensible) ideas, we appear to have solved the problem, although I think we’ve tried everything everyone suggested, plus a few more things besides.
Well, that’s not true. I’ve made the problem go away, which is not quite the same thing.
All our testing suggested that PC B being switched on was affecting PC A’s networking. This ’cause’ was not due to PC B’s networking (because the problem persists when it’s disconnected from the network) and not due to any interference from PC B’s monitor (the problem persists when it’s switched off).
The only way we could make the problem go away was by powering PC B from a different location (a power point on the opposite side of the room, via a very long extension lead). This suggests to me that the electrical cable used to power PC B was causing interference to the network cable connected to PC A or to the network cables in the ducting nearby, even though these two were not really in close proximity; certainly no more so than any other cables in the department.
So that’s an end to this peculiar little episode, I hope.