OK. I've managed to answer my question, so I'll put the info I gathered from a few places here to help out others.
At some point it appears my Z-net got a static IP address on the device itself (presumably a mis-click in the router settings when assigning it a static IP which should have been reserved in DHCP, NOT stored on the Z-net).
You can connect a keyboard and monitor on HDMI and watch as it logs on. I could see it getting the wrong IP address. Some people have said there is a prompt to press r during this bootup to reset the network settings, but I can't see this, so I let it go to the prompt and logged in.
There are also questions about which logon works. This one worked for me:
(Thanks to one of RJH's posts for that).
The rest of the info I got here:
You can just follow the steps (you can ignore the MathWorks-related bits. If they have something in brackets just type the command from within the brackets.
In short, I edited the interfaces file, changed static to DHCP and removed the 3 lines for the gateway, IP address and subnet mask. Saved, exited and rebooted and I'm back on DHCP and able to pick up an IP address.