1. Have you allowed AvastSvc.exe and avast.setup in your firewall? Double checked settings. and adjusted as suggested
2. Can you browse the internet on that pc? Yes I am talking to you from the pc concerned. Still getting the same message.
3. Set the connection as "direction connection(no proxy)" in settings(Right hand top corner in avast GUI) > updates > proxy settings > select direction connection(no proxy) Double checked settings. and adjusted as suggested
What other security software have you installed?

So, as I said, we still need to know about the security tools currently installed or that were installed in the past. The rest has been answered.

@maltacanary, try to follow my previous suggestions (clean browser cache, reset modem, reboot, try again), and come back with positive/negative feedback (including the answer for that question about security tools).