The Problem
Laptop (An ASUS G73S) does not show any indications of life when plugged into tested working charger. Previous owner reports that charging cable had to be rotated a special way in order to get the laptop to charge properly.
The Diagnosis
Laptop was disassembled and the DC input jack was tested. When probed, there was no continuity between the jack and the 19v rail on the motherboard. DC jack is not making contact due to cracked solder and needs to be repaired or replaced.
The Repair
The peg that the DC jack was manufactured with is too short, so in addition to re-soldering the connection, I added a small copper wire to extend the connection. While I had the laptop open, I also replaced the thermal paste and cleaned the ventilation.
The Results
Laptop functions perfectly and is now completely usable.