Thanks for the replies - been away for a few days:
Conan: It is FAT 32 formatted and works fine with my laptop (isn't it normally the other way around?) So it does rather point to my desktop. The other factor may be differing operating systems; my laptop is ME while my destop is XP. The USB 2 ports were a later addition to the machine - but it doesn't work with the original USB 1 ports either (while it does with the USB 1 port on the laptop).
The device is mains powered but 'Saab' has pointed out some power issues which I knew nothing about.
I think the problems are going to remain a mystery so I will try and cure them in cost order - first with a double USB lead and then with a powered hub. Fingers crossed