I have the same problem with Avast 4.8.
In my situation, the operating system is Windows Vista Service Pack 1. I've tried both official release 4.8 and the new beta version.
The problem occurs random, after reboot, the Web Shield does not work. Everything seems to be normal, except the browsing: nothing loads in Firefox, the website is reached, started to load but nothings come in, blank page and 0 files counted in Web Shield statistics. If I terminate the service, everything in back to normal. If a start again the service, the browsing is normal, again, but the Web Shield statistics are still stuck at 0.
At the next reboot, most of the time, everything will run very well again.
No other antivirus, antispyware, firewall or something like that.