Well what you describe isn't an avast function, it scans content and alerts to infection, it doesn't block and it (currently) doesn't have a firewall.
What is your firewall ?
The only thing I can think of is some sort of privacy function, like that in the zone alarm pro version. Or possibly some sort of conflict with another security application that also monitors web traffic.
So what other security software do you have installed ?
I know you said this computer came installed with avast, but has there been another AV installed at any time and if so what and how was it removed ?