begin
  Application.Initialize;
  Application.CreateForm(TMain, Main);
  App.Initialize;
  Main.Logon;
  Application.Run;
end.

procedure TMain.Logon;
  Show;
  Application.ProcessMessages;
  Login := TLogin.Create(Self);
  try
    if Login.ShowModal <> mrOk then Application.Terminate;
  finally
    Login.Free;
  end;
end;

procedure TAppEx.MainFormWndProc(var Message: TMessage);
begin
  case Message.Msg of
    WM_DESTROY:
    begin
      DefMainFormWndProc := nil;
    end;
    WM_ACTIVATE: //<----- добавляем -----
      with TWMActivate(Message) do
      begin
        if (Active in [WA_ACTIVE, WA_CLICKACTIVE]) then
        begin
          if IsWindowEnabled(Application.MainForm.Handle) then
            SetActiveWindow(Application.MainForm.Handle)
          else
            SetActiveWindow(Application.Handle);
        end;
      end;
    WM_SYSCOMMAND: //далее оставляем как было

  TAppEx = class(TObject)
  private
    //...
    procedure WMActivateApp(var Message: TWMActivateApp); message WM_ACTIVATEAPP; //добавить

implementation

//------------- процедура WMActivateApp --------
type
  TMainHandles = array[0..1] of THandle;

function GetMainWindows(Handle: HWND; Info: Pointer): BOOL; stdcall;
begin
  if (Handle = Application.Handle)
  or ((Application.MainForm <> nil) and (Handle = Application.MainForm.Handle)) then
    if TMainHandles(Info^)[0] = 0 then
      TMainHandles(Info^)[0] := Handle
    else
      TMainHandles(Info^)[1] := Handle;
  Result := True;
end;

procedure TAppEx.WMActivateApp(var Message: TWMActivateApp);
var
  wnds: TMainHandles;
  I: Integer;
  LastHandle: THandle;
begin
  inherited;
  with Message do
  begin
    if Active then
    begin
      FillChar(wnds, sizeof(wnds), 0);
      //запоминаем в каком порядке сейчас находятся два главных окна
      Windows.EnumWindows(@GetMainWindows, Longint(@wnds));
      LastHandle := 0;
      //переносим их в том же порядке на передний план
      for I := 0 to high(wnds) do
      begin
        if wnds[I] <> 0 then
          Windows.SetWindowPos(wnds[I], LastHandle, 0, 0, 0, 0,
            SWP_NOMOVE or SWP_NOSIZE or SWP_NOACTIVATE);
          LastHandle := wnds[i];
      end;
    end
  end;
end;

procedure TAppEx.MainFormWndProc(var Message: TMessage);
begin
  case Message.Msg of
    WM_DESTROY:
    begin
      DefMainFormWndProc := nil;
    end;
    WM_Activate:
     with TWMActivate(Message) do
      begin
        if (Active = WA_ACTIVE) and not IsWindowEnabled(Application.MainForm.Handle) then
         begin
           SetActiveWindow(Application.Handle);
           Message.Result := 0;
           Exit;
         end;
      end;
    WM_SYSCOMMAND:
    begin

  Application.MainFormOnTaskbar := True;