I think I figured out what I was trying to do.
1) I needed to set the “StartupUri” in the App.xaml to “Logon.xaml”, where Logon.xaml is my logon window.
2) in the LogonButton_Click event handler, I added the following
if (blnAuthenticateSuccessful) {
MainWindow main = new MainWindow();
App.Current.MainWindow = main;
this.Close();
main.Show();
}
This seems to accomplish what I want.