Was this the tool you used to remove Kaspersky ?
KIS6 Removal - http://support.kaspersky.com/downloads/kis6/kiskav6remove.zip.

When this problem occurs what avast processes are in the Windows Task Manager, they begin with ash or asw, see image.

What happens when you try to check your email, are there any error messages, if so can you post the complete text ?

Personally with the changes you have been making to attempt a resolution, I would suggest a clean install.

It would probably be best to download the latest version of avast http://www.avast.com/eng/programs.html and save it to your HDD, somewhere you can find it again. Use that when you reinstall.

Download the avast! Uninstall Utility, find it here and save it to your HDD so you can find it later.

Now, uninstall, reboot, run the uninstall utility, reboot, install, reboot.