Ok, I got it sorted myself and it was the ROM that was wrong as I'd suspected. I used the utility from 'Wugfresh' called Nexus Root Toolkit and it worked great. It was a big hassle getting my XP notepad to talk to the Nexus, that took ages, but it's useful to know you don't need a fast PC to to this. Apparently USB hassle with Windows and Nexus is normal but having downloaded USB drivers and eventually persuaded it to connect using MTP it all started to work, but it was a pain trying to figure it out. Wugfresh has tried to include as much info as possible so do take notice of the driver guide, step 1, which explains what you need for setup. I started to 'get it' after the fourth or fifth attempt of getting it to communicate. (It really is neat that you keep getting pop-ups reminding you what's happening and asking have you done the previous step ok and what might be wrong if it doesn't work.)
It's called Root toolkit, but it will reflash back to stock settings as well as rooting which I don't need. Once I loaded the Nexus with the right ROM the unwanted mobile stuff had all disappeared and everything was as it should be. I let it boot up and load load my apps and then used the utility again to make a backup. I don't know quite what is backed as I haven't used it. Still, it's not so hard to reload the ROM now I know how, so I can do that if I want anyway.
So having got this far I saw that Mr Wugfresh's util would also load a dev version of Android L, so I thought I'd give that a go and get to see it a few weeks earlier than waiting for the update, and that worked fine too, so that's now what I'm running and it seems great.
I'd done reading before and downloaded SDK and images and various stuff but this Toolkit doesn't need any of that and will download just what's needed as you go along. (Though you can pre-download the ROM image if you want to, which might be easier if you have a slow connection) So bottom line is many thanks (and some millibitcoins donation) to Wugfresh, his toolkit has saved my Nexus from having to go back to the dodgy repair shop at Asus again.