I’m not aware of any normal session having a “disconnecting” screen on shutdown. Perhaps you mean “Log off”? Try booting with minimal startup applications, eg Safe Mode or using msconfig to disable startup apps as there could be an application conflict.
I can only suggest again to check drivers are current, particular the video and network drivers as these are often the cause of systems hanging. Perhaps try an earlier version of Avast or uninstalling unneeded modules as per other forum thread instructions. If removing Avast definitely fixes the issue I’m afraid Tech Support is likely your best course of action here. Good Luck!