The mouse could be faulty.
Have you tried to manually install a driver for the USB device seen in Device Manager?
On the laptop, have you had an external (PS2) mouse installed previously? If so, delete it from the system.
If not, check that the BIOS is set to use an external mouse - it is usually possible to set the BIOS to only use the built-in pointer OR use internal and external.
Wouldn't explain why it doesn't work on your desktop though.
SD