That’s a somewhat bizarre thing for a shop to say for a “no crank” problem. Perhaps they mean that’s the least expensive way to address it. But there’s quite a few tests they can do to narrow the cause down. Here’s some ideas
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It’s pretty common this time of the year, early fall, to have complaints here of no cranks caused by the battery nearing the end of its life. As the ambient temperature cools off, that will show up a battery problem that didn’t exist in the summer. The ability of a weak battery to crank the engine is highly dependent on ambient temperature. If you live in a hot area, like Florida or New Orleans, 3 years is about how long a battery lasts. A shop can do a load test to determine if the battery is ok or not.
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The quickest way to figure out what’s causing a no-crank in my opinion is to measure the voltage at both starter motor terminals (the start and battery terminals). This must be measured during attempted cranking, with the key in start. If both measure 10.5 volts or above, and it doesn’t crank the engine, that’s almost always a defective starter motor. It could be a defective starter solenoid, but I think on your car the solenoid is part of the starter motor and would typically be addressed by just replacing the starter motor with a new one.