Most commonly it is the firewall blocking avast, but the win7 firewall has outbound protection disabled by default. So unless you enabled it, that shouldn't be the issue.
I don't know if the wow launcher/downloader is getting caught in the same issue, but we will try with the browser/web shield issue.
Do you use any proxy to connect to the internet ?
- also see Cause for apparent Web Shield blocking internet connection,
http://forum.avast.com/index.php?topic=57443.0. Confirm if your environment variables are correct and that the folders actually exist.
- check the BehaviorShield.txt file using notepad and see if there are any entries associated with the wow downloader/launcher and report your findings. c:\ProgramData\Alwil Software\Avast5\Report\BehaviorShield.txt