Mail doesn't show windows

Question

Setup my brand new iMac 21.5" with Mountain Lion (10.8.4) today and migrated from old iMac (10.6.8) Time Machine backup. The backup was made today just before the new startup so is absolutely current. Searched here and found many entries but they are all very old so not really relevant.
So once the (about 3 hour) migration had finished I had a new Computer and it all looked just like the old one (apps. and files etc.) I thought it was really simple but maybe I was too hasty...
Launched Mail and was told I needed to import my mail accounts to use this so selected OK (only other choice was cancel which quit the program). When I clicked OK it seemd to launch another copy of Mail, showing a seconf icon in the dock. It went through the process of importing all my old e-mails and then simply displayed nothing. Mail was running but no windows were visible.
Viewing Preferences shows all the migrated accounts correctly. Selecting New Message seems to work but typing an e-mail and sending has no effect. The message dissappears and no new windows appear. So I have no idea if it attempted to send or not but the recipient doesn't receive.
Choosing any other menu option such as 'File/New Viewer Window' or 'Window/Message Viewer' either quits or hangs where 'Force Quit' is the only option. Choosing 'Quit' from the dock doesn't do anything, nor does 'Cmd-Q' either. Quitting when Mail is running only works from the menu.
Looking in the Preferences folder there is NO 'com.apple.mail.plist' file but there is a file called 'com.apple.MailMigratorService.plist'.
Haven't checked everything else yet but most things I have checked seem to be OK, just Mail so far. I'm at a loss so would appreciate any help.

Answer 1

Back up all data. Don't continue unless you're sure you can restore from a backup, even if you're unable to log in.
This procedure will unlock all your user files (not system files) and reset their ownership and access-control lists to the default. If you've set special values for those attributes on any of your files, they will be reverted. In that case, either stop here, or be prepared to recreate the settings if necessary. Do so only after verifying that those settings didn't cause the problem. If none of this is meaningful to you, you don't need to worry about it.
Step 1
If you have more than one user account, and the one in question is not an administrator account, then temporarily promote it to administrator status in the Users & Groups preference pane. To do that, unlock the preference pane using the credentials of an administrator, check the box marked Allow user to administer this computer, then reboot. You can demote the problem account back to standard status when this step has been completed.
Enter the following command in the Terminal window in the same way as before (triple-click, copy, and paste):
{ sudo chflags -R nouchg,nouappnd ~ $TMPDIR.. ; sudo chown -R $UID:staff ~ $_ ; sudo chmod -R u+rwX ~ $_ ; chmod -R -N ~ $_ ; } 2> /dev/null
This time you'll be prompted for your login password, which won't be displayed when you type it. You may get a one-time warning to be careful. If you don’t have a login password, you’ll need to set one before you can run the command. If you see a message that your username "is not in the sudoers file," then you're not logged in as an administrator.
The command will take a noticeable amount of time to run. Wait for a new line ending in a dollar sign (“$”) to appear, then quit Terminal.
Step 2 (optional)
Take this step only if you have trouble with Step 1 or if it doesn't solve the problem.
Boot into Recovery. When the OS X Utilities screen appears, select
Utilities ▹ Terminal
from the menu bar. A Terminal window will open.
In the Terminal window, type this:
res
Press the tab key. The partial command you typed will automatically be completed to this:
resetpassword
Press return. A Reset Password window will open. You’re not  going to reset a password.
Select your boot volume ("Macintosh HD," unless you gave it a different name) if not already selected.
Select your username from the menu labeled Select the user account if not already selected.
Under Reset Home Directory Permissions and ACLs, click the Reset button.
Select
 ▹ Restart
from the menu bar.