There is indeed a PC card in there - it slides into a single-edge mount a bit bigger than that of a memory slot, but the same sort of idea, and there is a two-pin plug to remove on the other edge.
I withdrew the card and the queries in Device Manager cleared. So it was the right card.
I couldn't see a manufacturer's name on it but there were some numbers on some of the chips. I'll photograph it tonight - it's easy enough to remove. When I refitted the card the Device Manager queries came back.
Would it be worth deleting the PCI devices from the Device Manager, removing the card, firing up, closing down, refitting the PC card and seeing what happens? When I first had Win 95 (then Win ME) back in the day I used to bimble about doing that sort of thing, and, as if by magic, things used to start working. We've become rather spoilt with Win 7 and 10, I think.
Julie - that sounds like a plan: thanks.