The ports don't change for browsing no matter what avast version you are using.
How did you install avast Pro, clean install or insert avast Pro license into the free version to convert to avast Pro ?
Try a repair of avast:
XP - Add Remove programs, select 'avast! Anti-Virus,' click the Change/Remove button and select Repair, click next and follow.
Vista, win7 - Control Panel, Programs & Features, uninstall a program, select 'avast! Anti-Virus,' click the Uninstall/Change and select Repair, click next and follow.
You may need to reboot after the repair.
What is your operating system and firewall ?
Does it allow avastSvc.exe internet access ?
- If it does delete the entry for it and reconnect to the internet, this should force the firewall to ask permission again.