[dr. F.I.N.]

Код:

var
fs: TFileSteram;
ms: TMemoryStream;
begin
  fs := TFileStream.Create(<FileName>, fmOpenRead);
  fs.Seek(<startblock>, soFromBeginning);
  ms := TMemoryStream.Create;
  ms.CopyFrom(fs, <endblock> - <startblock> + 1);
  ms.Seek(0, soFromBeginning);
  Memo1.Lines.LoadFromFile(ms);
  ms.Free;
  fs.Free;
end;

Писал на коленке. Не проверял.