I was experiencing the same problems, I could not activate Avast and I could not access the internet. I tried the recommendations above and reinstalling fixed the activate Avast bottom ... it started normally but no internet. It was blocking it. When I uninstall Avast the internet would work then I'd reinstall and nothing. I've been using Avast for over 10 years and I am disappointed big time. I have purchased the Pro version in December and I have the Pro on 3 laptops ... but it does not work on 1 which is a windows 7, 64 bit. It worked prior to the latest update and it works now but I won't have internet...big time disappointed. I have now uninstalled it and install an alternative anti-virus. I have never had this problem with avast....ever.
The strange thing is the other laptops with the Pro version are also windows 7, 64 bit ... doesn't make any sense.