Автор: http://www.swissdelphicenter.ch

procedure TForm1.Button1Click(Sender: TObject);
 begin
   // Check whether DropedDown 
  if SendMessage(ComboBox1.Handle, CB_GETDROPPEDSTATE, 0, 0) <> 1 then
     // nop, so drop it 
    SendMessage(ComboBox1.Handle, CB_SHOWDROPDOWN, 1, 0);
 end;