Gmail and Google searches would be using the https protocol and as such secure connections aren’t redirected and scanned by avast’s web shield.

The most common cause of not being able to connect to the internet after an update is firewall blocking the avast changed components.

What is your 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.

However, the above would only be of use had you retained the latest avast version.