OK, so I have the NUC back together and it's working again. In fact this is being posted from it.
But was an ongoing drama, just to replace the therm past between the processor and the heat-sink! I took the NUC into a computer shop and David - whom I spoke to over the phone yesterday - tried to get the lead attached but couldn't, because the pin on the ead was BENT. I probably did that yesterday trying to reattach it. The good news is that it's the backup WiFi antenna and I probably don't need it anyway, especially as I prefer to use LAN at home.
Anyway, I got home, and after having lunch and laying with the dog, proceeded to put the rest of the NUC together. I made several mistakes: leaving the memory cards out (oops), nd putting screws that hold the main board in the wrong holes (and later blocking the longer screws that are attached to the base) being the most annoying. But it's back together again and working. This means I can finally get back to working on SECONDS.
The next time I need to do something like this, I'm taking the NUC to a shop and paying someone to do it!