OK that sounds more like a firewall blocking issue, but it could be something else you didn't tell us what version of avast you are using ? 4.7.827 is the current latest build and there have some issues with an earlier build. please let us know, just saying the latest 4.7 version unfortunately doesn't state what build version.
If it is firewall blocking (strange if you have disabled ZA), check the program access in ZA and see if there is an entry for avast.setup. If so delete it and try a manual update, ZA should ask permission for avast.setup, allow access to the internet and see if that resolves the problem.