You didn't mention the OS as that determines if its firewall even has outbound protection, XP's has none, vista and win7 has outbound protection, but is disabled by default.
- Do you connect to the internet using a proxy (web accelerator, ISP, etc.) if so you would have to co-ordinate that with the web shield proxy ?
- Try this also if the above doesn't make a difference - From the avastUI, Settings, Updates, Proxy Settings, set it to Direct connection (no proxy), see image.