A password hasn't been required in the past, even if one were set, to uninstall using add remove programs, etc.
The uninstall utility should be run from safe mode, avast doesn't run in safe mode.
Are you trying to uninstall from a limited user account ?
That I believe would fail, so you would need to either run it as the administrator or the account that you used to install it.
I haven't heard of this 'advanced' settings password protection either as the password feature is basically designed to stop the avast settings being changed. Can you post an image of this 'advanced' settings password blocking window.