Verificando o seu endereço IP

A fonte do projeto principal ficará algo como:

implementation

 uses Winsock;

 {$R *.DFM}

 procedure TForm1.FormCreate(Sender: TObject);

var

  wVersionRequested : WORD;

  wsaData : TWSAData;

begin

  wVersionRequested := MAKEWORD(1, 1);

  WSAStartup(wVersionRequested, wsaData);

end;

 procedure TForm1.FormDestroy(Sender: TObject);

begin

  WSACleanup;

end;

 procedure TForm1.BtnIPClick(Sender: TObject);

var

  p : PHostEnt;

  s : array[0..128] of char;

  p2 : pchar;

begin

  GetHostName(@s, 128);

  p := GetHostByName(@s);

  Memo1.Lines.Add(p^.h_Name);

  p2 := iNet_ntoa(PInAddr(p^.h_addr_list^)^);

  Memo1.Lines.Add(p2);

end;

 end.