Well I would start by not installing an old version of avast, I can only assume you didn’t get it directly from avast.
The network connectivity would appear to be correct:
What is your firewall ?
Does it allow ashWebSv.exe internet access ?
If it does delete the entry for it and do a manual update and reconnect to the internet, this will force the firewall to ask permission again.
You could do a manual program update (right click the avast ‘a’ icon), select Updating, Program Update of course your firewall might block avast.setup the avast update process, same drill as above if it does.