I experienced what you described commonly before we even used Avast, but only at start-up. Windows 7 in particular seems to like to have the yellow ! over the network activity a lot when it makes no sense.
Does it only happen when you first log in, or does it stay on the entire time you have Web Shield on? Seems to me more logical that Network Shield or Firewall would directly affect your Network Connection status alert, rather than Web Shield. Perhaps I do not know enough how Web Shield works.
/* Thomas */