Update, sort of, as promised.
As you can see, back on line and BOTH machines are able to log on - hooray!!
Problem is, I have no idea what happened. It wasn't anything offered by the Orange 'help' service, 'cos it still wasn't working when I lost their phone contact with a flat battery.
Anyway, it does work, after a fashion and marginally faster than a dial-up connection but constant drop-outs, freezes etc.
Thank you all again for the tips and suggestions.