Update: Again, thanks to all and Milo in particular.
I found a couple of 'spare' PC hours and
I tried the CatRoot2 folder reste (NB The advice is NOT to fiddle with 'Catroot'). Had to stop ZA to get the cryptoservice to stop, but even then a rename of CatRoot2 did nothing.
Ran the remove programme (ALL VERSIONS)
I then ran CCcleaner which found pages of stuff.
Ran sfc /scannnow
Last reboot offered me 3.5 as an 'optional' install - following the link from Phineas I decided that would be enough and it installed!
A succession of SPs etc have followed and all have gone on ok.
I think a temporary sigh of relief!