Did you make sure, that all your email identities and accounts are set up correctly for KMail2 and Akonadi?
Do you use IMAP or POP3?
In the case of POP3 do a web search for "KMail2 POP3 spool"!
As you say, you "imported" your email to KMail, I guess, your problem is a failed migration. Unfortunately, migration from Kmail to a completely different mail client turns out to be a lot easier than to KMail2. The problems are related to the fact, that KMail2 relies heavily on Akonadi.
I'd recommend that try to set up KMail2 from scratch. However, one problem with recent KMail versions relying on Akonadi is that configuration files are distributed over several locations, so it may easily have happened that you just forgot to backup and restore one of these files, and that could cause the problems you describe.
To leave your emails intact, but enable a fresh setup, you might try the following (essentially taken from the FAQ
Log out from KDE and stop Akonadi (e. g. reboot your system).
Log in to another window manager or desktop or console (don't log in to KDE, at this stage!), and try the following:
$ rm -rf ~/.local/akonadi
$ rm -rf ~/.config/akonadi
$ rm -rf .cache
$ rm -rf /tmp/kde*
$ rm -rf /var/tmp/kde*
$ rm -rf ~/.kde/apps/emailidentities
$ rm -rf /tmp/akonadi*
This erases Akonadi setup and caches that might interfere with your attempts to configure KMail2, and should give you the chance for a clean, fresh email setup.
Probably unnecesaary, but just to make sure it works, reboot again.
Log in to KDE fire up KMail2 and start to set up your identities and accounts.
Without more detail it's hard to tell, what actually causes your problem, but the above should either solve it or help to track it down, at least.