Do you have another device, such as a laptop, that you can connect via ethernet to check that the ethernet ports are working correctly?
Also try another ethernet cable if you have one.
Next I would power off your BT Box, then factory reset the SH2 by inserting and holding something in the reset hole in the back. When it's fully back up and connected switch on your BT Box and see how it goes then.
If it still doesn't connect try holding the Standby button on the BT Box for about 8 seconds until it reboots. The final suggestion is to use Maintenance Mode on your BT Box to do a factory reset. Select your model number and follow the instructions here.
I have tried everything up to maintenance mode. I seem to be unable to get this to work. Box is a DTR-T4000. I hold down the down arrow to get Enter Maintenance Mode Y/N (Y:POWER). I pressed the power button on the box... but nothing different happens and it just goes straight to set up mode!
I would think so. How far does it go through Set Up? If you press the blue Home button on your remote does it bring up the menu? If it does, go to Settings and scroll to the bottom, there's a Factory Reset option there.
If not then you're best calling BT, it's going to be a pain getting through for obvious reasons but at least you've tried everything you can at your end so it 'should' be a quick call to send you a replacement box.
It turns on - asks to set up - first thing it does is try connect to the internet - fails and asks me to check connections. Home button does nothing unfortunately.
I’ve yet to plug an aerial in it yet - but can’t see how that would stop it setting up.
The aerial won't affect it, I use my T4000 without one. You've tried all of the common fixes so I'd suggest contacting BT, it sounds like a faulty box to me.
New boxed arrived and working as expected.
Second problem is that it won’t run off my Tp-link “Wi-fi extender” Ethernet socket. Obviously a separate issue. Is this a compatibility thing or a set up issue with my extended?
I would not expect it to work on a wifi extender, as the wireless network would not be able to carry the multicast data needed to deliver subscription channels.
The best option would be to ask BT for some mini connectors.