Ok, without knowing the operating system (Vista) at all well, nor having experienced the problem, my considerations will go something like this:
If Spybots' TeaTimer were active, and causing it, it would have popped an alert.
AdAware runs a background service even when the program isn't running. (Betcha didn't know that.) It probably isn't the culprit, though, as the service is mainly there to facilitate updates, AFAIK.
Windows Defender runs resident, unless you've disabled it. It might possibly be blocking the update, but it's doubtful. Worth checking the quarantine/log, though, just to be sure.
Normally I'd suspect the firewall blocking the connection by a "new" unknown program, but unless you've configured the firewall to do this, it's doubtful.
So what I'd suggest, from this domain of partial uncertainty, is to let the Avast update occur, reboot as commanded, and if the problem again manifests, try carrying out a repair install, from the control panel. (It's one of the options available when you click "change/remove" in what used to be called "add/remove programs".)
Another thing to think about is the UAC in vista. Which I think defaults to limiting adding/removing software to the equivalent of a limited user, unless it's deactivated for the update?
Maybe someone Vize in the Vayz of Vizta can comment.
But at least try the "repair install".
[EDIT] PS After my Avast auto updated, I also immediately got the definitions update. So that aspect isn't unusual. The problem has got to be to do with something blocking the connection following the program update.