Thanks for your quick reply. I'm answering your part by part:
Please, check:
1. Your subscription (license) status.
2. The system time and date.
3. If your firewall settings and allow avast.setup to connect. Maybe you should 'remove' avast.setup entry, try to update, receiving a new alert from the firewall, allowing it and checking it to remember.
4. Check your proxy settings into avast!: Settings > Updates > Proxy Settings. Try switching from "Auto-detect" to "No proxy".
1. Avast 4.8 was activated up to November 2010 before upgrading to 5.0. No problems with that.
2. My system synchronizes itself to clock.psu.edu every time I reboot.
3. Yes, I've had more than one entry for it. I tried removing all of them and allowing Avast full Internet access when prompted. Didn't work.
4. Already done. No luck.
0x20000004 error is a "proxy down" error, i.e., server unreachable (or, in other words, "cannot connect to the updating server"). Is there any other Firewall installed on the machine besides Windows own firewall? Have you had any previous anti-virus program installed on this computer before installing avast? The last way is check your hosts file to see if there are any entries that could be blocking avast's update servers. A blank "default" configuration of the windows hosts file should basically have only one entry (127.0.0.1 localhost).
Yes, I've had Ashampoo Firewall 1.20. No prevoous Antivirus (besides Avast 4.

Avast has been my only antivirus for many years. My hosts file only has the localhost entry.
Now I've removed Ashampoo Firewall and replaced it with PCTools FW. Avast is updating now, but I wonder why can't I use Ashampoo as firewall.
Thanks