обработчик события DrawColumnCell, там пишешь:

procedure TForm1.DBGrid1DrawColumnCell(Sender: TObject; const Rect: TRect;
DataCol: Integer; Column: TColumn; State: TGridDrawState);
begin
if column.Field.FieldName='LastName' then
if (column.Field.AsString)='Nelson' then
begin
dbgrid1.Canvas.Brush.Color:=clBlack;
dbgrid1.Canvas.Rectangle(rect);
dbgrid1.Canvas.Font.Color:=clWhite;
dbgrid1.Canvas.TextOut(rect.Left+1,rect.Top+1,column.Field.AsString);
dbgrid1.Canvas.Font.Color:=clBlack;
end;
end;