@doktornotor: My ISP service hasn't been an issue before.
@Tech: That's how I did it. I uninstalled avast, ran the McAfee uninstaller, then reinstalled Avast. I've uninstalled and reinstalled Avast at least once since then as well. Doesn't seem to help. Every "fix" so far has only been temporary. The problem keeps coming back every other day or so. Yesterday it went away on its own - when I started up the computer, I could access the internet just fine. Today, though, it had come back - when I started up the computer, I had to first disable the Web Shield before I could access the internet.
EDIT: Also, for the record, I already had Win 7 SP1 installed on this machine prior to downloading and installing Avast. So my case isn't like some of the others' where Avast 6 was working fine until they installed SP1.