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Check my guide MacBook power cord 5 pins Magsafe connector and cable Replacement
You wrote the details the way I should have. but there is no point in just repeating all you said, Thanks ;-)
The picture shows the parts from step 4 (third picture) and 25.
I am sorry to tell you, you will have to open the phone again.
My guess is to take a look at the step 29 to make sure the contacts are placed properly
Are you talking about the ends of the cable ?
If it is the case, just strip a little bit no longer than 3/16" of an inch ( like 3mm ) you have to make sure it is not too long; you can see at the step 8, there is no room on the other side of the board.
And heat it to apply soldering on it so it looks like the picture, it is easy to insert and it weld solidly.