Some additional information - If I disable the "Web Shield" in Avast, this problem does not happen.
I can then open any browser (and also start Parallels, which I think is equivalent to a network connection). No problem. All of this is with wireless connected.
Then I can activate the "Web Shield" and still no problem.
However, if I then go anywhere in any browser the problem starts and continues.
So I am guessing that com.avast.daemon is related to "Web Shield" and it is interacting incorrectly with something that correlates with network activity.
As far as I know, there have been no changes to network connections.
Does this help to localize the problem? Thanks