I am now back at my desk and can give a more precise description:
1. Under "Universal Serial Bus controllers" within Device manager, when I plug in the Galileo I have the message "Unknown USB Device (Device Descriptor Request Failed)"
2. A similar Windows pop-up message is shown at the base of the desktop.
3. When I right click on the message in device manager, I then opt for "Update Driver Software".
4. I can then browse to "C:\arduino-1.5.3-Intel.1.0.4\hardware\arduino\x86\tools" as suggested above.
5. I then immediately get the message "The best driver software for your device is already installed" but the dialog box header still reads "Unknown USB Device (Device Descriptor Request Failed)", as does a second message within that dialog box.
I have contacted Dell Technical Support and updated everything to the latest available on the laptop, but still I see the same problem. As previously mentioned, the device is recognised on an old Windows 7 machine, so the cables and connections are proven ok.