I have to twist the cord right where it meets the jack. Do the cords get crimped inside and cause these problems?
I had the same problem 4 months ago. I took it to a local computer repair (mom & pop type) shop and they fixed it for me overnight. It was, indeed, the jack. It cost $115 and it's worked beautifully since. They also told me it's a tedious repair and that's why many places won't do it.
No crimp inside
Most likely point of power cord failure is where the cord connects into the plug (jack) that you insert into the laptop. Through lots of bending and manipulation (I kind of doubt you are doing this) it becomes frayed at that point. Gets frayed within where you cannot see it