Bourne,
Deep breath from me - how can I put this - I don't have an IT set up like a Microsoft Testing Lab i.e. I don't have the capability to "Before re-installing it, if you can get a computer which has installed the Outlook 2013 client (and it works well), try to setup your Office 365 account on another Outlook 2013 client and check the result." If you're happy to post me through a laptop from Microsoft with Windows 7 installed and then Outlook 2013 also installed, I'll happily have a go at your suggestion.
I'm hoping today to try to delete the profiles and then re-set up a single profile, as you suggested. If that doesn't work, then I'll uninstall and re-install Outlook 2013 (trying to remember which COM plug-ins cause it to crash, so I have to turn them off in Outlook safe mode).
In terms of using the Autodiscover - I have tried this. I did this with the second profile that I was told to set up by Chris, but I got the same error. Today, when I re-set up the profile and then if required uninstall / de-install Outlook 2013, I will use the auto-discover in both of these cases.
Another question for you - what happens if this doesn't work? How long does this saga go on for? How do we get it fixed? Are you willing to pay to send out a Microsoft technician to the computer to get it fixed quickly, so we don't have these days of to'ing and fro'ing? I'm running a business here and Microsoft 365 is currently killing my productivity, when it was supposed to be increasing it!
Paul.