Just saw the end of your video and now i'm 100% sure it is the battery. I thought you had a battery in the car, but you dont. When you jump a car normally, the good car's alternator charges the dead battery and supplies the extra current needed to start the dead battery.
Without a battery in the dead car, you are completely relying on the other car's battery to supply 100% of the current. Depending on the length and gauge of the cable, the voltage loss is 20-25%.
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