DNS communication should not be blocked by avast, but could you please disable
Network Shield provider when you'll find out you can't resolve site names ? The best is, to run "nslookup
www.google.com" from command line window and copy&paste results here (it communicates directly to your DNS so it'd tell us more than the fact that your browser is unable to resolve a host address).
Thanks.
In spite of that, we still think it's not our fault
- at least, we dont know how we could block DNS.