How do I use Internet accounts to add accounts to mail in mavericks

Question

I used migration Assistant to Migrate to a new Imac(late 2013), The new machine was 10.8.4 so the very first thing I did was add an account so I could update. I suspect this was the root cause of my problem because then when I migrated the account I had to rename it
Everything worked fine except for mail. Note under library/mail I still had a 45Gb folder.
My internet accounts had a list of all the mail accounts I used to have but mail itself was empty. All the accounts are imap so I have not lost mail.
Trying things mentioned on the forum I tried deleting the accounts under internet accounts and re-adding, and I tried importing from the mail folder. Importing sort of worked but created a big mess of mail under a import folder.
Where I am right now. I deleted everything including my library/mail folder.
I go to mail. I do add acount, I add a icloud account, I select paul...me.com It adds the account.
I then can go to accounts and see my me.com address with mail ticked.
And nothing. Mail just sits their blank.
Now I can trick it it into adding one account, when everything is blank, instead of giving me the new system preferences internet accounts it gives me the old accounts from mail 10.8, I can then add 1 account under their and it will work., As soon as it has one account it then goes back to giving me the system preference internet accounts which just lets me add acounts but does not work with mail.

Answer 1

Yes it all works under a new user. Thank you.
At this point the simplest solution is probably to put everything else from the old user into the new one, hopefully without breaking anything else.