ElementStyle error for DataGridComboBoxColumn in WPF

TextBlockComboBox is an internal type to DataGridComboBoxColumn. I also don't know how to get that type styled but you can trick DataGridComboBoxColumn.ElementStyle by using a ComboBox style that looks like a TextBlock:

<Style x:Key="TextBlockComboBoxStyle"
       TargetType="{x:Type ComboBox}" BasedOn="{StaticResource {x:Type ComboBox}}">
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="{x:Type ComboBox}">
                <TextBlock Text="{TemplateBinding Text}"
                           Style="{StaticResource {x:Type TextBlock}}" />
            </ControlTemplate>
        </Setter.Value>
    </Setter>
</Style>

In the above style I use a globally-defined TextBlock style defined elsewhere and bind the Text property of the ComboBox. Finally you can use the style like so:

<DataGridComboBoxColumn ElementStyle="{StaticResource TextBlockComboBoxStyle}"
                        EditingElementStyle="{StaticResource {x:Type ComboBox}}" />

The EditingElementStyle in this case is again a globally-defined ComboBox style defined elsewhere.

ElementStyle in this case should be the type of ComboBox. We have two types of DataGrid, which it operates - DataGridRow and DataGridCell, the first is a line, the second cell. Therefore, by default, everything is composed of cells of the type DataGridCell not TextBlock's.

To determine the type of another column, use DataGridTemplateColumn. Therefore DataGridComboBoxColumn maybe is defined as:

<DataGridTemplateColumn Width="1.5*" IsReadOnly="False" Header="Position2">
    <DataGridTemplateColumn.CellTemplate>
        <DataTemplate>
            <ComboBox x:Name="ComboBoxColumn" />
        </DataTemplate>
    </DataGridTemplateColumn.CellTemplate>
</DataGridTemplateColumn>

With this set can be any type of control.

In your case, you need to create a style for DataGridCell:

<Style x:Key="StyleForCell" TargetType="{x:Type DataGridCell}">
    <Setter Property="Background" Value="Green" />
</Style>

And using like this:

<DataGridComboBoxColumn x:Name="ComboBoxColumn" 
                        CellStyle="{StaticResource StyleForCell}"
                        Header="Position"
                        SelectedItemBinding="{Binding Position}" />