I have missed this thread if the thread starter want the answer.
From his nickname i see that he is for greece.
From his router i can imagine that he is use OTEnet Dsl.
I had the same problem in the past with web browsing.
The problem Is that the dns servers dont resolve the ips.
I REMOVE The NORTON dns servers and the problem never come again.
I dont know if our isp has problem with avast+norton dns together but i kept avast and i removed the northon dns and i have no problem from then.
It took me 10 days of testing , if i use avast + opendns i have no problem if i use norton dns +avast i cant browse after 5 minutes.
Maybe some incobatibility with our isp and northon.
I am having the very same problem. Just installed the latest version of the Avast!Internet Security and it cut my 3G connection.
I made some experimentation and found that if you install Avast! without the Firewall (you can choose in the installation) you can use the other features with no problems. Worth a try until they make a fix.