Fixing my Black and Decker 14.4V Battery Charger

UPDATE!!! – I revisited this repair. Read the history below then go here:
Black and Decker 14.4V Battery Charger Repair (revisited and improved)
History: I own a 14.4V Black and Decker cordless drill with a laser. My wife bought it for me for some reason; probably because I liked it, and she wanted me to build something.
Measuring the voltage drop across the 10Ohm resistor

Measuring the voltage drop across the 10Ohm resistor

A little over a year ago, I was given a 14.4V B&D Firestorm drill that quit working. The Firestorm charger quit charging, as verified by the transformer windings giving me an open reading on the “Oh-meter”. To clarify, “‘Oh’, that’s why it isn’t charging.”
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How to Read a Datasheet: A Beginner’s Guide

Manufacturers publish datasheets for everything that they make so that we can use the parts as they are intended. How many watts can my transistor dissipate? What pin is the ground pin? How do I communicate with this RTC? Every day in electronics someone is asking how something works. It’s really easy to ask someone else, and then wait for their reply and hope they are right, but we are given tools to use. Nevertheless, it’s a whole new world to try and figure it out on your own.
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