The most likely cause of this is your firewall (or remnants of your previous AV) blocking avast functions and that 3rd party support should damn well know that and is well within the bounds of the free support.

This is usually how we determine what the problem might be and it is usually resolved quickly and for free:
What is your operating system and firewall ?
Does it allow avastSvc.exe internet access ?

  • If it does delete the entry for it and reconnect to the internet, this should force the firewall to ask permission again.

Have (or did) you another Anti-Virus installed in this system, if so what was it and how did you get rid of it ?

These questions generally give an indication of why you can’t connect with your browser or email.