Try to bump start it. If it starts without difficulty you can only blame your starter / battery / earth. If it doesn't, you have bigger problems.
 
Even when he's got it to start, it runs really rough. The starting system may not be 100% but I think the real problem is elsewhere.
 
Watch his vid - with that much air going into the injector pump, its not worth chasing other things (yet!)

: )
 
It's also worth checking the glow plug relay, I had one that fired the glow plugs until the starter was turned, at that point it stopped powering the plugs, this made cold starting a problem and run ruff until worm.
But as Julian has said, you need to track down that air leak.
 
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.
 
You have a big air leak there. Thats not helping. Looking at the spill pipes they are wet and you still have the horrible plastic final pipe going back to the pump. They crack with age and need getting rid of. Go to Halfords and get a reel of their small bore fuel piping - it's just sufficient to do all the inter injector spills and the return hose. Also check that the cap on the number 4 injector that has no spill pipe is sound.

Mine was an absolute pig to start and run and it was nothing more than a small hole in the plastic pipe weeping diesel out and letting air in. Swapping them transformed the car.
 

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