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So let's see, you are a female Canadian fiction writer...... your first name is Margaret, right??
(Okay, that's an old, old joke, and our readers would probably have to be Canadian to get it.......)
Are you going to tell the reader exactly the make, model and year of the car.... just so we can state an accurate failure which is consistent with the equipment that car would have?
If not, here are a couple of chronic problems which would prevent a car from starting, yet can be fixed in seconds.
My first choice is that he has to whack the starter motor with a metal rod (perhaps a lug wrench he keeps under the hood for such a purpose) while his buddy is actually turning the key....... This is a real, valid temporary fix for some worn-out starters. Sometimes, if they have a sticky Bendix drive or work commutator or brushes, they simply will do nothing at all when the key is turned, unless they receive a sharp jolt.
This would apply to virtually all cars, except post-1995 Cadillacs and the Oldsmobile Aurora (possibly others, too)..... you simply cannot reach their starters to whack them.
The next failure is a damaged battery terminal. Sometimes, if the terminals are a little loose due to stripped threads on the terminal, corrosion can build up, creating a poor electrical contact. This means when you turn the key to start, nothing happens, or you get a clicking/groaning sound. One can wiggle a loose terminal for a couple of seconds to temporarily improve the connection, allowing the engine to start.
Please note, this would be good for most older cars. But a few cars, like Audis, have the battery under the back seat, not under the hood. Also, a few, like late-90's Chryslers (Concorde, Intrepid) have no easy access to the battery terminals.