I found the problem, and it's SQL Server's insane paranoia. In Studio 2005, you have to set package security to EncryptSesnitiveWithPassword, then set a password.
In SQL Server, you can schedule the package after entering the package password. However, you'll STILL have to go to the connection manager settings and manuall ADD the database passwords - because it can't use the passwords from the package.
Once jumping through all those wonderful hoops, I can run the packages.
This kind of stuff makes me miss the old school DTS!