I don't know if the problem is the power cord.....
But any power cord problem will not occur just anywhere along the length of the cord. It will occur where it connects. To the wall or to the laptop. Wall is less likely.
I would remove the battery. Then boot up into the bios. Start wiggling the cord at the the two connection points and see what kills your laptop's power.
I have to twist the cord right where it meets the jack. Do the cords get crimped inside and cause these problems?