I have the solution, which came from me asking on the libusb site.
I came to the conclusion that the libusb-win32 stuff I have was causing trouble, but I did not know how. I therefore asked on the libusb forum
(https://lists.sourceforge.net/lists/lis ... in32-devel
, June 2010, "Libusb incompatibility with PicoScope??") and I got the answer I needed.
libusb-win32 is a package of USB goodies for the PC. It allows me to write my own USB firmware on a microcontroller and interface it to my PC using the libusb drivers. That bit works fine.
However, there is also a libusb "filter". I did not know what that was, but the recommendation was that I should install it, so I did. It turns out that this software attempts to replace all USB drivers for all USB kit. Mostly this works, so if a new USB device that the PC has never seen before is plugged in, this filter software intercepts it and provides libusb as a suitable driver. No need to pre-load CDs, etc.
Unfortunately there are still some bugs in the filter software, and it seems to have tried to use the libusb driver AS WELL AS the PicoScope driver. Confusion then reigned and it all fell over.
The solution is to disable the libusb filter.
[(Start Menu->LibUSB-Win32->Disable Filter (admin only)]
Once I did that, the PicoScope worked fine. Fortunately, my other USB kit works fine too, probably falling back on its own drivers. Some other bug may come out of the woodwork as I start to stress the system, but it all looks good so far.