IMHO, there are several factors involved in any troubleshooting problem. First and not least is the experience level of the tech. Less experience generally translates into more 'red herring' chases and less productivity. Electrical problems can be some of the most vexing problems, particularly on the high voltage size of things where you can measure 1/2 volts at all terminals. The important thing to keep in mind when dealing with any electrical issue is that just like you are moving toward professional HVAC status, there are electrical technicians and electrical engineers who are professionals in that one science alone. You must be an all around pro. That is, you've got to know electrical, airflow, refrigeration, gas, plumbing to name the basics. So being an expert in all phases can take years and years. So the average time I'd expect a 5-year tech to find a problem like the one you were given would be 15-30 minutes. If you find the chopped off wire right away, it's easy. Generally, the way to minimize you time for electrical problems is to do what I call a 'bracketing' procedure.
Start at the front end, such as at the power source or transformer, depending on the indications of the system. You didn't say if you were working with 24VAC or 120VAC or 240VAC??? But let's assume it's 24VAC; do I have primary voltage? If yes, move on. If No, you've found your issue. Do I have secondary voltage? If yes, then move to the end and check for voltage. If No, then you've found your problem. Check for volts coming out of the transformer, then check for volts at the contactor. If you've got volts at the transformer and not at that contactor, what's between them? Safeties? T-stat? The speed with which your mind will work through these steps increases with each experience. So don't despair. Keep studying and you'll come out on top sooner or later. We all went through it. None of use were born knowing this stuff. a
If YOU want change, YOU have to first change.
If you are waiting for the 'other guy' to change first, just remember, you're the 'other guy's' other guy. To continue to expect real change when you keep acting the same way as always, is folly. Won't happen. Real change will only happen when a majority of the people change the way they vote!