Magsafe2 not charging after repaired the wire
You’re getting the wrong voltage.  You should be seeing 3V not .5V.  Once connected to the Mac, it will sense the 3V then “request” the full 18V. 

What you measured was the incoming power of the mains so you “know” that it’s getting AC in. The problem lots on the DC side of things (after the rectifier) where something has gone bad. 

These voltages are listed on Pinoutguide.com and on Wikipedia (6.86V for MagSafe and 3V for MagSafe 2)

What’s wrong specifically?  You could have a blown capacitor, resistor or even an IC. You would need the schematics to see which line is sending the 3V and then make the diagnosis and repair. My thoughts are that something shorted with the damaged wire before you embarked on the repair. 

It’s probably safer and cheaper to just replace charger and be done with it.