[SAWaGE]

Вот, переделал. Заработало!

Код:

const
  FILEPATH = 'log.txt';
var
  logs: TStringList;
  Str : string;
  i: integer;
begin
  logs := TStringList.Create;
  try
    if not FileExists(FILEPATH) then Exit;
    logs.LoadFromFile(FILEPATH);
    Str := Copy(logs.Text, 1, Pos(#13#10, logs.Text) + 2);
    if (Pos(' ' + GetUserFromWindows + ' ', str) = 0) and
       (Pos(' ' + GetUserFromWindows + #13, str) = 0) then
    begin
      for i := 0 to logs.Count - 1 do
        logs.Strings[i] := logs.Strings[i] + ' ' + GetUserFromWindows;
        logs.SaveToFile(FILEPATH);
    end;
  finally
    logs.Free;
  end;
end;

Nyctos Kasignete, благодарю за помощь!