I had the exact same problem as Rbdawg (and some others), including the weird start-ups, no connectivity, etc....though mine didn't resolve as his did (though I made a similar attempt). Couldn't connect through my built-in network adapter, couldn't connect even with a wireless USB adapter (while other machines in the house still could)...tried everything, including trying rollbacks/updates/disable/re-enable of network adapter through the device manager, countless restarts, hard resets of router and modem...
I finally, as an act of desperation, uninstalled my on-board network adapter, uninstalled the Avast items that appeared under the Network Adapter menu in Device Manager, completely uninstalled the on-board network adapter and then downloaded/reinstalled the newest driver installer for it (even though it had already been up to date), and now it is FINALLY working. I'm still waiting for a response to my own post though (regarding whether the Firewall is now functioning correctly, after having removed the Avast items that were appearing in the Device Manager under the Network Adapter header). Considering an uninstall/reinstall of Avast, but trying to hold out for some kind of response to my post before I bother doing that.
Good luck man. My computer was offline for nearly a week before I finally got this thing SOMEWHAT resolved.
As an aside, my main wireless router is bricked...or at least it is tenaciously not working...even after hard resets, power-downs, etc...can't see how this could have anything to do with my computer or Avast, though the issue occurred simultaneously...right now I'm using an old 54MBPS router that I luckily had not thrown out when I got a new one.
Still have love for Avast, but wish there was clearer documentation regarding the Firewall/Device Manager stuff.