OK, I've worked out what the problem was, and how to solve it, but I'm not at all sure how it happened.
I noticed on my work PC that the visible DCIM folders were 'grayed out' - i.e. marked as hidden system files. (It just happened that on my home PC I didn't have explorer set to show hidden files).
The folder properties dialogue wouldn't let me uncheck the hidden option, so I ended up transferring the photos off, and then using the camera 'format' function.
After which, everything works again on my home PC.