In the most recent adaptation of War of The Worlds, at one point everyones cars stopped working. Except for the protagonists, which had just been repaired. Was this ever explained?
The mechanic was fixing the car the moment the EM pulse was fired, and replaced the solenoid after it happened, meaning the solenoid wasn't destroyed by the pulse and the car worked. Cruise's character realizes this and tells the mechanic to replace the solenoids on the stalled cars to fix them.
Now I don't know much about the mechanics of internal combustion engines, so I can't really vouch on how accurate this would be in real life.
Unless there has been some major change in spark plug tech, even connected to the system its unlikely you could get enough power through the cables to fry them before the cables exploded. The solenoid is a couple of very long wires coiled around a fero core. Its an electromagnet that takes low amps through the switch when you engage it to connect a high amp switch for starting the vehicle. If an EMP would fry any basic electrical system it would fry electromagnets. The thing I'm uncertain of is if it would make any real difference if the solenoid was connected or not. And if not being connected would protect it I would think not being engaged should as well, so the only cars that should need it replaced would have been those attempting to start their engines as the EMP occurred. The thing most likely to happen is that electronics would fry due to the voltage spike throughout the vehicle's wiring. And that would be a problem even if the engine was off but may not be a problem for spares laying around.