Thanks for the suggestions, all.
They had tried system restore, but it hadn't worked.
It arrived here this evening, and I had a look. I was fortunate, it had legacy ports so I could use the mouse at least in normal mode. Any USB device I tried to add, including memory sticks and other USB keyboards and mice wouldn't install a driver. I tried deleting the existing drivers and it would still fail.
It was set to only search locally for drivers, so I wondered if this wasn't helping, but even when forced to look online it wouldn't load any drivers. The message came back for everything: drivers have failed to install properly.
I did notice they hadn't been allowing windows updates so there were fifty or so outstanding. I thought I'd let them do there stuff before carrying on trying to sort the problem. However, just installing them allowed or actually carried out the reinstallation of the relevant drivers, and everything started to work.
So, all in all, an easy if time consuming fix. Best part of three hours and 250 meg of updates later, and it's all healthy again.