Unfortunately for you, this is likely an issue with the importing of old data.
Now, it is possible that you just have some rather large mailboxes, and the new system is simply trying to index all those messages. So if you let it run overnight or so, it might start working on its own. If not, then you'll probably need to wipe out the .plist files for Mail.app. This will mean that you have to set up all your accounts again and you may lose some messages.
I'm not sure if Mozilla Thunderbird will import Mail.app mailboxes or not, but it might be an option. Import the mailboxes into Thunderbird, and then back into Mail.app after.
I recently upgraded my Intel Mac from 10.4.11 up to 10.5.6
All other apps appear to work fine other than Mail.
Now, I no longer get a splash screen or a mail page.
The Mail app shows in the menu bar but nothing works and it
will not shut down unless forced.
Mail version is 3.5. Is this a common problem after upgrading?