As far as I know, Avast doesn't make firewalls. Any chance you're using another firewall?
A good point Neg, the free version certainly doesn't have a firewall.

When I encounter weird internet connectivity issues I generally run LSPFIX from the cexx organisation. It could be some sort of Winsock2 stack corruption.

http://cexx.org/lspfix.htm

Please read the instructions very carefully