Handle with care
These situations can actually be made very rewarding.
I started out as a humble in-the-home TV repairman (yes it was that long ago) and soon learned to make soothing commiserating noises. Once things had calmed down, I'd quietly ask what they would like me to put on the job ticket. So, "Not switched on" became "Loss of power". This almost always worked like a charm, and on repeat calls I even had customers saying they'd wait if I wasn't available on that day.
I carried that policy on when I moved into industrial electronics (where you also needed to quickly establish who was really in charge), and have made some good friends over the years. Also, your name gets known. It's amusing when you get a puzzled look from your boss, as a new customer calls up and and gruffly says says "Can you send Will - he seems to know what he's doing."