Simple window switching example with windows passing data to one another. Also shows a working TestStack.White test.

App.xaml

<Application x:Class="LoginExample.App"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:local="clr-namespace:LoginExample"
             StartupUri="StartingWindow.xaml">
    <Application.Resources></Application.Resources>
</Application>

App.xaml.cs

using System.Windows;

namespace LoginExample
{
    public partial class App : Application
    {
        public int loginCount = 0;
    }
}

LoggedInWindow.xaml

<Window x:Class="LoginExample.LoggedInWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:LoginExample"
        mc:Ignorable="d"
        Title="LoggedInWindow" Height="450" Width="800">
    <StackPanel>
        <TextBlock>Username:</TextBlock>
        <TextBlock Name="username" />
        <TextBlock>Password:</TextBlock>
        <TextBlock Name="password" />
        <TextBlock>Total logins:</TextBlock>
        <TextBlock Name="loginCount" />
        <Button Content="Logout"
                Name="Logout"
                Click="Logout_Click" />
    </StackPanel>
</Window>

LoggedInWindow.xaml.cs

using System.Windows;

namespace LoginExample
{
    public partial class LoggedInWindow : Window
    {
        public string currentUsername;
        public string currentPassword;

        public LoggedInWindow()
        {
            InitializeComponent();
            Loaded += LoggedInWindow_Loaded;
        }

        private void LoggedInWindow_Loaded(object sender, RoutedEventArgs e)
        {
            if (currentUsername != null && currentUsername.Length > 0)
            {
                username.Text = currentUsername;
            }

            if (currentPassword != null && currentPassword.Length > 0)
            {
                password.Text = currentPassword;
            }

            loginCount.Text = ((App)Application.Current).loginCount.ToString();
        }

        private void Logout_Click(object sender, RoutedEventArgs e)
        {
            var startingWindow = new StartingWindow();
            App.Current.MainWindow = startingWindow;
            Close();
            startingWindow.Show();
        }
    }
}

StartingWindow.xaml

<Window x:Class="LoginExample.StartingWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:LoginExample"
        mc:Ignorable="d"
        Title="MainWindow" Height="450" Width="800">
    <StackPanel VerticalAlignment="Center" HorizontalAlignment="Center">
        <Grid Width="200"
              Height="50"
              >
            <Grid.ColumnDefinitions>
                <ColumnDefinition Width="*" />
                <ColumnDefinition Width="2*" />
            </Grid.ColumnDefinitions>
            <Grid.RowDefinitions>
                <RowDefinition />
                <RowDefinition />
            </Grid.RowDefinitions>
            <TextBlock Grid.Row="0"
                       Grid.Column="0"
                       Text="Username" />
            <TextBox Grid.Row="0"
                     Grid.Column="1"
                     Name="username" />
            <TextBlock Grid.Row="1"
                       Grid.Column="0"
                       Text="Password" />
            <PasswordBox Grid.Row="1"
                     Grid.Column="1"
                     Name="password" />
        </Grid>
        
        <Button Content="Login"
                Click="Button_Click" />
    </StackPanel>
    
</Window>

StartingWindow.xaml.cs

using System.Windows;

namespace LoginExample
{
    public partial class StartingWindow : Window
    {
        public StartingWindow()
        {
            InitializeComponent();
        }

        private void Button_Click(object sender, RoutedEventArgs e)
        {
            if (Authenticate())
            {
                var loggedInWindow = new LoggedInWindow()
                {
                    currentUsername = username.Text,
                    currentPassword = password.Password
                };
                
                App.Current.MainWindow = loggedInWindow;

                // global mutable state. you can't stop me from writing, running, and using this code. deal with it. 
                ((App)Application.Current).loginCount++;

                Close();
                loggedInWindow.Show();
            }
            else
            {
                MessageBox.Show("Invalid username/password");
            }
        }
        
        private bool Authenticate()
        {
            return username.Text.Equals("warren") && password.Password.Equals("farts");
        }
    }
}

UnitTest1.cs

using Microsoft.VisualStudio.TestTools.UnitTesting;
using TestStack.White;
using TestStack.White.Factory;
using TestStack.White.UIItems;
using TestStack.White.UIItems.Finders;
using TestStack.White.UIItems.WindowItems;

namespace LoginExampleUITests
{
    [TestClass]
    public class UnitTest1
    {
        Application application;

        [TestMethod]
        public void TestLogin()
        {
            application = Application.Launch(@"C:\Users\Warren\source\repos\LoginExample\LoginExample\bin\Debug\LoginExample.exe");
            Window window = application.GetWindow("Login", InitializeOption.NoCache);

            TextBox textBox = (TextBox)window.Get(SearchCriteria.ByAutomationId("username"));
            textBox.Text = "warren";

            TextBox textBox2 = (TextBox)window.Get(SearchCriteria.ByAutomationId("password"));
            textBox2.Text = "farts";

            Button button = window.Get<Button>("LoginButton");
            button.Click();

            Window window2 = application.GetWindow("Logged In", InitializeOption.NoCache);
            Button button2 = window2.Get<Button>("Logout");
            button2.Click();
        }

        [TestCleanup]
        public void CloseApplication()
        {
            if (application != null) application.Kill();
        }
    }
}