What is your OS? Are you using the latest (.889) version of Avast!? What firewall are you using?
Couple things to try to get more conflict information for the developers:
1. There have been a few reported residual issues with the Behavior Shield. Go to Programs and Features, select Avast, uncheck behavior shield to remove it temporarily and see if that fixes the problem.
2. Do an uninstall of Avast! in safe mode with the Avast! uninstall utility. Then a custom reinstall using only the file shield. If things work, try adding back the Behavior Shield, Network Shield, etc. from Programs and Features.