Just a blind idea, but it is easy to try.
Avast main GUI -> web shield -> EXPERT settings -> "..."well known browsers only".
Avast main GUI -> settings -> troubleshooting -> "load avast service after other system services".
If you have firewall rules, delete all rules related to Avast (avastsvc.exe, avastui.exe and avast.setup).
Save and reboot. Then test. Your firewall (if you have one) should be set in "learn mode" (or however it is called) so to rebuild the rules for Avast.
If these settings don't work for you, please revert them back to what they were before.
Other shields might be related, but let's try those settings first.