[ecfisa]

Hola cocute.

Te hice un ejemplo simple (a modo de guía).

Código Delphi [-]
...
implementation

procedure TForm1.FileListBox1Click(Sender: TObject);
var
  i, it: Integer;
  o, d: TPoint;
begin
  d:= WebBrowser1.ClientOrigin;
  o:= ScreenToClient(Mouse.CursorPos);
  it:= FileListBox1.ItemAtPos(o, True)-1;
  o:= Mouse.CursorPos;
  if it <> -1 then
  begin
    FileListBox1.BeginDrag(True);
    i:= o.X;
    repeat
      SetCursorPos(i, d.Y +10);
      Inc(i, 4); 
      Sleep(1);
    until i > d.X+10;
    Application.ProcessMessages;
    FileListBox1.EndDrag(True);
    Mouse.CursorPos:= o;
 end;
end;

procedure TForm1.WebBrowser1DragOver(Sender, Source: TObject; X, Y: Integer;
  State: TDragState; var Accept: Boolean);
begin
  Accept:= Source is TFileListBox;
end;

procedure TForm1.WebBrowser1DragDrop(Sender, Source: TObject; X, Y: Integer);
begin
  WebBrowser1.Navigate(TFileListBox(Source).FileName);
end;

Saludos