Hi, David. I've put together a sample window that does this using triggers on the TextBox.Style:
<Window x:Class="WpfApplication1.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1">
<Window.Resources>
<SolidColorBrush x:Key="IsCheckedColor" Color="DarkGray" />
</Window.Resources>
<StackPanel>
<TextBox x:Name="textbox" Margin="36" Height="24" >
<TextBox.Style>
<Style TargetType="TextBox">
<Setter Property="Background" Value="White" />
<Style.Triggers>
<DataTrigger Binding="{Binding IsChecked, ElementName=checkbox}" Value="True" >
<Setter Property="Background" Value="{StaticResource IsCheckedColor}" />
<Setter Property="IsEnabled" Value="False" />
</DataTrigger>
</Style.Triggers>
</Style>
</TextBox.Style>
</TextBox>
<CheckBox x:Name="checkbox" Content="Click Me" Height="24" Margin="36"/>
</StackPanel>
</Window>
You can't use a Trigger to change another control's properties, but you can use them to change a control's properties based on something else, like a DataContext or another control.
Each control can have a Triggers collection, but this can only contain EventTriggers. In a Style you can use plain Trigger which can be used to control animation, as well as DataTrigger, which I've used in this sample to control the TextBox settings based on the properties of the CheckBox.
Notice that I've also used a Setter outside of the Triggers collection to set the default value, and I don't need a second Setter for when the CheckBox is not checked -- it just goes back to the "default" state.
edit - how to change background of disabled TextBox
I do this in Blend, but if you don't have Blend you can of course put the XAML in directly. This has to do with controls states. As the TextBox transitions among Normal, MouseOver, and Disabled, you can animate changes to the appearance. In this case we use an animation of virtually zero duration, so the change is immediate.
Add the following to the StackPanel:
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="VisualStateGroup">
<VisualState x:Name="Disabled">
<Storyboard>
<ColorAnimationUsingKeyFrames BeginTime="00:00:00" Duration="00:00:00.0010000" Storyboard.TargetName="textbox" Storyboard.TargetProperty="(Panel.Background).(SolidColorBrush.Color)">
<SplineColorKeyFrame KeyTime="00:00:00" Value="{StaticResource IsCheckedColor}"/>
</ColorAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>