Avast includes a firewall, so go into the app (you probably have to click "more tools" to see the firewall) and change the settings to allow the apps you want to have net access to have it.
If you are using the firewall in "whitelist" mode then any new app you install will be unable to use the internet unless you enable that app in the firewall. Unlike some specialist firewall apps I don't recall Avast asking when you install a new app, so if you set it up this way and forgot about it it can catch you out.