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Can avast.setup (a temporary file created while avast is being updated) allowed to connect the internet?
Do you use a proxy filter?
If not, make sure your browser is not set to "Work Offline" (this option is generally in the File menu). If it doesn't help, try switching the proxy settings from "Auto-detect" to "No proxy" (I'm assuming you're not connecting to the Internet via proxy).
Left click the avast icon > Settings
Update (Basic) > Details > Proxy