>>>It maybe be your principle account, if you switch main account to another account, you maybe able to delete that trouble one.
>>
>>Unfortunately I am unable to remove my old account. When I try to do so, I get this message (see attached). I don't know how to remove all old Exchange accounts first.
>
>The message seems to indicate that it is still your primary account.

Now I can not even get my account to work :( It shows 'working offline'. I can access it from Web interface, though.

UPDATE. So after several unsuccessful tries I went ahead and deleted both accounts and then re-created my main new account. Of course, I lost all my original account info, I believe, but at least I don't have problem anymore (hopefully).

So the lesson learned is that when we setup a new account we have to remove all old accounts otherwise they will bite you...