The problem is most likely related to the ‘the scan secure connections’ option in Web Shield, turn that off an it will work.
How to turn that off via terminal? I have no idea, at worst you might try making a script that changes the .plist.
As Sysadmin, you probably won’t like the way it works anyway, avast is able to scan secure connections because it installs a root certificate (you might want to check if the cert is being correctly installed and trusted, this would explain why the web isn’t working) and then the web shield is a proxy that acts as a MITM decrypting the contents, scanning, and then encrypting again using the installed cert.