Ok, I've managed to reinstall the antivirus without having to uninstall the firewall, but now the firewall doesn't seem to be working, so that is most likely the problem here.
Since the ZoneAlarm Firewall + Avast Free combo doesn't seem to be working anymore, is there something you can suggest? Maybe Comodo Free Firewall or a different antivirus? Or maybe some setting I should change or some exception I have to add to make them work together again? I would really prefer to avoid changing if possible.