Have the same problem - after upgrading avast Internet Security from 2013 to 2014, both IE (11) and Firefox (25.0) stopped working, they simply do NOT OPEN ANY SITEs anymore, as long as the WEB SHIELD inside avast IS 2014 is on.
Accordingly, the solution to that is fairly simple - disable the web shield.
The sad part is, that I am paying for this product, so I would like to actually use all its features - not having to disable some, so that I can continue working as I did until the upgrade to avast IS 2014
This is the first time I am disappointed from avast IS .. but I guess, there is a first time for everything.
PS: when first disabling the web shield for 10 minutes, and then, when seeing, that it "fixed the problem", I tried to disable it permanently, the whole avast IS interface just hangs on me, for minutes on now, with 2 non-responsitive windows: the main avast IS window, and the Settings -> Active protection window .. both not responding even to standard windows "Close window" clicks, repeatedly.
OS version: Windows 7 Ultimate SP1
That makes me strongly want to downgrade to avast IS 2013 again - let's see if I find the good old version somewhere around on the download page ..