Re: help me out with a few problems?
You didn´t mention which four wheel drive system you have. Looking at the video it seems to have the 4.7L with 5-45RFE transmission, which i believe only comes with Quadra Trac II or Quadra Drive. Both use the same T-case, the NV247. Besides the chain can stretch too much and touch the housing bottom (there is no tensioner in there and when getting stretched too much it will rub on the housing and wear the aluminum away), it also has a progressive coupler which transfers part of the torque to the front wheels when a speed difference between front and rear prop shafts occurs. This coupler in many cases is shot, preventing the 4all time to work. In that case only 4lo works. For this four wheel drive system its very important that front and rear wheels wear evenly, because a diameter difference between front and rear wheels will cause a rotational speed difference between the front and rear prop shafts and will cause the progressive coupler to be activated all the time and wear the clutch away rapidly.
So if you want to stay with this type of T-case, its probably better to get a good used one. What many other did is swapping in a NV242 T-case. Here you can choose between full time 2 wheel or four wheel drive. This swap also requires a new rear prop shaft and T-case shift lever.
Getting a used T-case is still no guarantee on the state of the chain and/or progressive coupler.
So if your T-case works ok, then maybe a new chain would be the cheapest option.