My Internet Shield was blocking almost every web-site (including Avast Support ironically!) but I eventually found the solution in a thread here - although the process was a little different as I have avast!Internet Security 2014.9.0.2008. Go to Settings - Active Protection - Web Shield click the little wheel and make sure the box for Scan Traffic from well-Known Browser Processes is checked.
I have absolutely no idea why this should work and this solution has probably been noted many times - all I can say is it appears to be working for me 