Well what version of windows, makes a difference ?
However, generally there is either zero outbound checking (winXP) or it is disabled by default (Vista & win7), so unless you enabled outbound checking in those which have it, then it shouldn't be the cause.
Connections to those don't use http, port 80 so wouldn't be going through the web shield proxy.
Try a repair of avast. Add Remove programs, select 'avast! Anti-Virus,' click the Change/Remove button and scroll down to Repair, click next and follow.
What browser are you using ?
Have you tried another browser to see if it works with that ?