Jennifer thanks again! O.K. I'm hoping this will be our last correspondence on this item.The field I'm after is PARCELID and it is not the same as OBJECTID.  It is a unique field/key that corresponsed to our Code Enforcement database.  I think MySelectionGraphicLayers is a GraphicsLayer; Here's my code.
private void esriTools_ToolbarItemClicked(object sender, ESRI.ArcGIS.Client.Toolkit.SelectedToolbarItemArgs e)
        {
            switch (e.Index)
            {
                case 0: // Point
                    _drawSurface.DrawMode = DrawMode.Point;
                    break;
                case 1: // Polyline
                    _drawSurface.DrawMode = DrawMode.Polyline;
                    break;
                case 2: // Polygon
                    _drawSurface.DrawMode = DrawMode.Polygon;
                    break;
                case 3: // Rectangle
                    _drawSurface.DrawMode = DrawMode.Rectangle;
                    break;
                default: // Clear
                    _drawSurface.DrawMode = DrawMode.None;
                    GraphicsLayer selectionGraphicslayer = Map.Layers["MySelectionGraphicsLayer"] as GraphicsLayer;
                    selectionGraphicslayer.ClearGraphics();
                    QueryDetailsDataGrid.ItemsSource = null;
                    ResultsDisplay.IsExpanded = true;
                    break;
            }
            _drawSurface.IsEnabled = (_drawSurface.DrawMode != DrawMode.None);
            StatusTextBlock.Text = e.Item.Text;
        }
        private void MyDrawSurface_DrawComplete(object sender, ESRI.ArcGIS.Client.DrawEventArgs args)
        {
            GraphicsLayer selectionGraphicslayer = Map.Layers["MySelectionGraphicsLayer"] as GraphicsLayer;
            selectionGraphicslayer.ClearGraphics();
            QueryTask queryTask = new QueryTask("http://SERVERNAME/ArcGIS/rest/services/Parcels/MapServer/0")
            queryTask.ExecuteCompleted += QueryTask_ExecuteCompleted;
            queryTask.Failed += QueryTask_Failed;
            Query query = new ESRI.ArcGIS.Client.Tasks.Query();
            query.OutFields.Add("*");
            query.Geometry = args.Geometry;
            query.ReturnGeometry = true;
            _queryTask.ExecuteAsync(query);
        }
        private void QueryTask_ExecuteCompleted(object sender, ESRI.ArcGIS.Client.Tasks.QueryEventArgs args)
        {
            FeatureSet featureSet = args.FeatureSet;
            if (featureSet == null || featureSet.Features.Count < 1)
            {
                MessageBox.Show("No features retured from query");
                return;
            }
            GraphicsLayer graphicsLayer = Map.Layers["MySelectionGraphicsLayer"] as GraphicsLayer;
            if (featureSet != null && featureSet.Features.Count > 0)
            {
                foreach (Graphic feature in featureSet.Features)
                {
                    feature.Symbol = LayoutRoot.Resources["ResultsFillSymbol"] as FillSymbol;
                    graphicsLayer.Graphics.Insert(0, feature);
                }
            }
            //ResultsDisplay.Visibility = Visibility.Visible;
            ResultsDisplay.IsExpanded = true;
            _drawSurface.IsEnabled = false;
        }
        private void QueryTask_Failed(object sender, TaskFailedEventArgs args)
        {
            MessageBox.Show("Query failed: " + args.Error);
        }
Right now I would just like to just display and pass the PARCELID to a textblock that will display in my app; once I get this working I can move on to the next piece.Here's what I'm trying and It is not working out.
        private void FeatureDataGrid_SelectionChanged(object sender, SelectionChangedEventArgs e)
        {
           
            var graphics = (sender as ESRI.ArcGIS.Client.Toolkit.FeatureDataGrid).SelectedGraphics;
            foreach (var g in graphics)
            {
                // get id 
                var id = g.Attributes["PARCELID"];
                // TODO: retrieve outside data for this id
                PARCELIDPASS.Text = string.Format("The ParcelID passed is {1}", id);
                break;
            }
        }
In my XAML I have:
    <TextBlock x:Name="PARCELIDPASS" Text="" Foreground="Red" FontWeight="SemiBold" Margin="0,5,0,5" HorizontalAlignment="Center" TextWrapping="Wrap"/>