I post a PTC link in my eariler reply, It is a Resistors, Non-li

http://www.vishay.com/resistors-non-linear/ptc/

Refer to above link, for your NB, it should be a ~20V <4A range PTC.

BTW, I didn't see your cable, PTC inside just my guess from my expereince and your description. I hope you can figureout if there is something in your cable create the voltage drop and by-pass it then you are close to boot your NB. Good luck.