Grrr. Darned internet is down again, but I now know it is not the ISP's fault.
They sent a proper technician to the house yesterday, who fiddled with lots of test equipment and determined that the signal entering the house is strong as strong. But by the time it reaches the RJ thingie socket into which the modem/router is plugged, it is weak as a kitten. The wiring, which runs inside the wall, as so often with vital services in Italy, is probably as old as the building (70 years) and had deteriorated.
Fortunately I have an electrician coming tomorrow, because I figured that the simple answer would be to create a new RJ thingie socket where the line comes into the house. Can I wait that long? Might need to try and jury rig something myself.
Grrr.