procedure TForm1.Timer1Timer(Sender: TObject);
Var
  H : HWND;
begin
  H:=ShellExecute(Handle, PChar('open'), PChar('http://www.yandex.ru/'), Nil, Nil, SW_SHOWNORMAL);
  DestroyWindow(H);
end;

procedure TForm1.Timer1Timer(Sender: TObject);
Var
  H : HWND;
begin
  H:=WinExec('explorer.exe http://www.yandex.ru/', SW_SHOWNORMAL);
  DestroyWindow(H);
end;

unit New;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;

type
  TForm1 = class(TForm)
    Button1: TButton;
    Button2: TButton;
    Button3: TButton;
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

var
  SearchHandle:HWND;

function EnumProc(h:HWND; lParam:DWord):boolean; stdcall;
var
  ProcessId, z:cardinal;
begin
Result:=True;
GetWindowThreadProcessId(h, ProcessId);
If ProcessId=lParam then
begin
  SearchHandle:=h;
  Result:=False;
end;
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  si:STARTUPINFO;
  pi:PROCESS_INFORMATION;
  buf:array[1..100] of char;
begin
ZeroMemory(@si, sizeof(si));
si.cb:=SizeOf(si);
CreateProcess(nil, 'Путь к экзешнику\MyExe.exe', nil, nil, false,
    0, nil, nil, si, pi);
SearchHandle:=0;
While SearchHandle=0 do
begin
  EnumWindows(@EnumProc, pi.dwProcessId);
  Application.ProcessMessages;
end;
SendMessage(SearchHandle, WM_CLOSE, 0, 0);
end;

end.

...
si.cb:=SizeOf(si);
si.wShowWindow:=SW_HIDE;
si.cb:=SizeOf(si);
CreateProcess(nil, 'MyExe.exe', nil, nil, false, 0, nil, nil, si, pi);
...