Lithium battery conversion

Assuming you are plugged in and the converter (aka: charger) is powered up. The 14.6v sounds reasonable it should be the same measured across the terminals on the converter and on the cable ends when they get to the battery box. 

If you measure 0v at the cable ends at the battery box, there is presumably a break in one or both of the cables. Check for loose connections and if none are obvious, your multimeter should have a continuity setting. With the converter powered down, check each cable for continuity. Once you find a bad one, check for cuts in the insulation, breaks in the wire or loose connections until you are certain, the cables are good all the way from the converter to the battery box...at that point, the voltage across the cable ends at the battery box should match the voltage at the converter terminals.