Thanks for your help.
No - Our other Mac cannot see the phone. When I connected it to an old (10 yr old) PC laptop - a Dell Latitude D610 - a 'New Hardware Wizard' flashed up. It searched the internet but could not find software. When the cable was removed, it made a noise. This told me that the cable was OK.
I cannot fathom why the Mac cannot see it.
Neither Mac has it on Finder, and it is not in My Computer on the PC. It still got the 'New Hardware Wizard' up on the PC.