procedure TfrmOtchetD.ButtonOkClick(Sender: TObject);
begin
    NewThread:=TNewThread.Create(true);
    NewThread.FreeOnTerminate:=true;
    NewThread.Priority:=tpLower;
    NewThread.Resume;

    dstOtchetD.Open;
    frmOtchetD.ProgressBarD.Style := pbstNormal;
    NewThread.Start;

    while not NewThread.Terminated do
    begin
       Application.ProcessMessages;
       Sleep(50);
    end;
    ProgressBarD.Visible := False;
end;

destructor TNewThread.Destroy;
begin
  self:= nil;
  inherited;
end;

  TForm1 = class(TForm)
  ...
  private
    FVar, FCnt: PtrUInt;
    FIsAllow: Boolean;
...
procedure TForm1.btnStartClick(Sender: TObject);
var Li: PtrInt;
begin
  Inc(FCnt);
  Label1.Caption:= Format('Кнопка Start нажата: %d раз',[FCnt]);

  if not FIsAllow then Exit;
  FIsAllow:= False;
  FVar:= 0;

  for Li := SmallInt.MinValue to SmallInt.MaxValue do
  begin
    if FIsAllow then Break;
    Inc(FVar);
    //Sleep(10);
    Label2.Caption:= Format('Текущее значение FVar: %d',[FVar]);
    Label3.Caption:= Format('Текущее значение счетчика итераций Li: %d',[Li]);
    Application.ProcessMessages;
  end;

  if not FIsAllow then
  begin
    FCnt:= 0;
    ShowMessage(IntToStr(FVar));
  end;
  FIsAllow:= True; 
end;

procedure TForm1.FormClose(Sender: TObject; var CloseAction: TCloseAction);
begin
  FIsAllow:= True;
end;