Webrep extension has nothing to do with net access, webrep serves one purpose only, to show you the Web Reputation ranking (according to Avast!) of sites when you google for them. But lets leave that aside, by just saying that webrep is a red herring here.
Of course it's possible, as you can expect, most users have no problem whatsoever connecting to the internet using their browsers and Avast!, or else there would be no Avast! by now. You make a lot of assumptions based not only on webrep but on your bad experience, the first of that assumptions is that everyone else or most people had your problem, this isn't true, I never had that problem.
If we come down from those assumptions and accept this is a rare or exotic behaviour, then we can actually go thru the specifics of your environment. Let me give you some examples: Do you have any firewall (like little snitch) blocking access to avast? Do you have any proxy configured?
As of right now, your post boils down to "I cannot connect to the internet and I don't know why" and everything else is a bitter rant based on a construction of assumptions on top of assumptions that you force people to read if they have a genuine intent of helping a fellow man (my case).
