What Does "Local Computer Resources" Comprise in Task Scheduler?
Solution 1:
My experience indicates that ADS authentication with a remote Domain Server exceeds "local computer resources", so you can't run a task as an ADS username without storing a password. You can of course create a local user on that machine who will be authenticated locally without Task Scheduler storing the password.
However, check out the discussion of "S4U" here: http://technet.microsoft.com/en-us/library/cc722152.aspx
Maybe it's not actually the authentication, but the fact that our ADS users' homedirs are on network servers.
Solution 2:
From my understanding, local resources will be local drives in this case. And so task scheduler will not be able to access any network resource. And about storing password option, this TechNet article might help you.