Actually, I reported the issue to Avast tech support and here is the reply:
In fact, avast! doesn't block the Internet pages browsing if your computer is configured properly. If you have this kind of problem and turning avast! off helps, it means that one part of avast!, the Web Shield, doesn't have access to the Internet. The solution is easy - allow the Web Shield to connect to Internet in your firewall.
Ensure that the Web Shield process ashWebSv.exe or aswWebSv.exe is listed as an application that is permitted to connect to the web in your firewall configuration. It also needs a permission to act as a server and accept incoming connections from localhost (the local machine) on TCP port 12080.
Some firewall do require you have a rule for incoming connection from localhost. Please check that too.
The summary: it is NOT avast! that blocks the browsing, but your incorrectly adjusted firewall.
If you don't know how to change the appropriate settings, I recommend you to turn the Web Shield off. Don't worry, it will not reduce the security level provided by avast!.
1) Click on the blue a-ball icon in system tray to show the Resident protection settings
2) Click on the DETAILS button
3) In left pane, click on WEB SHIELD provider
4) In right pane, click on TERMINATE
5) Confirm the permanent changes with OK button(s)
So, I'm going to try this and post back to the board. Seems like lots of people viewed this post, so I presume others may need a fix too.