If you have uninstalled avast then there should be no conflict or interaction so I can’t understand why this is happening.

What is your OS ?
What errors are you getting when you can’t log in to email boxes ?
Please post the full text or a screenshot of the error.

What is your firewall ?

Download the avast! Uninstall Utility, find it here and save it to your HDD so you can find it later. Run the utility that should ensure that any remnants are removed.