<DataGrid AutoGenerateColumns="True" Name="dataGrid1">
        <DataGrid.CellStyle>
            <Style TargetType="{x:Type DataGridCell}">
                <Style.Triggers>
                    <DataTrigger Binding="{Binding Name}" Value="Billy Bob" >
                        <Setter Property="Background" Value="Red" />
                    </DataTrigger>
                </Style.Triggers>
            </Style>
        </DataGrid.CellStyle>
    </DataGrid>

<DataGrid AutoGenerateColumns="False" Name="dataGrid1">
        <DataGrid.Resources>
            <Style TargetType="{x:Type DataGridCell}" x:Key="MyCellStyle">
                <Setter Property="Foreground" Value="Green"/>
            </Style>
        </DataGrid.Resources>
        ...

col.CellStyle = (Style)dataGrid1.Resources("MyCellStyle");

public class ArtistNameConverter : IValueConverter
{
    public object Convert(object value, Type targetType,
        object parameter, CultureInfo culture)
    {
        try
        {
            return value.ToString().StartsWith(parameter.ToString());
        }
        catch
        {
            return false;
        }
    }

    public object ConvertBack(object value, Type targetType,
        object parameter, CultureInfo culture)
    {
        throw new NotImplementedException();
    }
}

<DataGrid AutoGenerateColumns="True" Name="dataGrid1">
        <DataGrid.Resources>
            <converters:ArtistNameConverter x:Key="ArtistNameConverter"></converters:ArtistNameConverter>
        </DataGrid.Resources>
        <DataGrid.CellStyle>
            <Style TargetType="{x:Type DataGridCell}">
                <Style.Triggers>
                    <DataTrigger Binding="{Binding ArtistName, Converter={StaticResource ArtistNameConverter}, ConverterParameter=a}" Value="True" >
                        <Setter Property="Background" Value="Red" />
                    </DataTrigger>
                </Style.Triggers>
            </Style>
        </DataGrid.CellStyle>
    </DataGrid>

public class ArtistNameConverter : IMultiValueConverter
{
    public object Convert(object[] values, Type targetType, object parameter,
        System.Globalization.CultureInfo culture)
    {
        try
        {
            return values[0].ToString().StartsWith(values[1].ToString());
        }
        catch
        {
            return false;
        }
    }

    public object[] ConvertBack(object value, Type[] targetTypes, object parameter,
        System.Globalization.CultureInfo culture)
    {
        throw new NotImplementedException();
    }
}

<DataGrid.CellStyle>
            <Style TargetType="{x:Type DataGridCell}">
                <Style.Triggers>
                    <DataTrigger Value="True" >
                        <DataTrigger.Binding>
                            <MultiBinding Converter="{StaticResource ArtistNameConverter}">
                                <Binding Path="ArtistName" />
                                <Binding Mode="OneWay" ElementName="FirstLetter" Path="Text" />
                            </MultiBinding>
                        </DataTrigger.Binding>
                        <Setter Property="Background" Value="Red" />
                    </DataTrigger>
                </Style.Triggers>
            </Style>
        </DataGrid.CellStyle>