had a telephone conversation with a competent person at the company which sold me my old computer (and the newest laptop) and fitted the network card as a repair.
therefore tested out some more things about the new router and the lack of viable ethernet comms alongside someone with more of a clue than a TalkTalk person. This includes IP configuration data (setting & changing & checking) to establish that there is basic wire connectivity recognised at the router sockets but only full communication with laptop.
the World Of Computers bod was similarly outraged to me about the way the new TalkTalk router is happy to do 192.168.1.1 setup via WiFi and also slightly upset that the new TalkTalk router didn't have any little lights on its ethernet ports to show powered connection existed.
noting that the old VirginMedia SuperHub, still sat uselessly on a table next to me, does have those little LEDs to indicate ethernet port activity. It's another example of companies not making them like they used to do (and should).
tested https vs http when using 192.168.1.1 (doesn't help) and manual vs dynamic IP address (doesn't help) and even wired (aeroplane in-flight mode) comms from the laptop - which does work for internet access and shows it's possible for packets to get through the ethernet from the laptop (unlike the old computer).
to do the last and most impossible test which requires moving the old computer out and around enough to be able to wire a new cable between the back of it and the new router - in case it's an issue of using all 4 wire pairs on the ethernet socket.
apparently that's a thing which really has changed in the past few years. However, he admits that my current long cable (fixed in place across the room to connect the zones and only 5-ish years old) ought to be correct as a CAT6 one and he also believes that the network card from them should be using all pairs.
so it's very much a clutching-at-straws test. Rather like changing the boot-up order (so the new router is the first thing that the old PC sees) would be.
not looking forward to the trauma of moving everything around, having to scrabble under & behind furniture, risking breaking something (equipment or me!) and creating a new trip hazard on the floor.