My 300 tdi starts so fast you can't really hear the starter. That said if u have replaced the battery and it is still hard to start but cranking quickly, it must be as stated possible air leak, suggesting lack of fuel getting to the cylinders, or injectors not working properly either. The valves sounded as if clattering in video Not likely to be glow plugs as ive read and experienced that, u seldom need them, as these engines will start even when thermometer plummets. Lift pump as suggested is a possibility. Good luck.