According to the notes I took at NBC school (Nuclear, Biological & Chemical warfare), EMP will fry the electronics of most any civilian vehicle line of sight to the detonation, especially the rather delicate computers associated with the starter and regulating the engine especially in the more upscale cars. In other words, anything with electronic start or even electronic fuel injection won't work. I'm guessing if you have a 1975 or prior Ford Bronco, you're ok. Maybe one of the original IH Scout 4x4's.
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Hi, Ex! The Ford diesels are a good bet through the period they used mechanical fuel injection. No ignition system, as you know, other than the simple resistance glow plugs. These were basically farm-tractor primitive without any kind of digital electronics. For example, I have an '84 E-350 cube van outfitted as a bug-out rig with three types of alternative fuels for heating and cooking plus solar and gasoline for the generators. The box is hardened and can't be easily broken into. Well stocked with particulate and organic respirators. Parked a few hundred feet from a uncrowded highway leading off to the desert/mountains.
The gasoline would run out after a few days and that would be the end of the A/C in the box. But there would be plenty of clean warm or cool water for showers and drinking . Speaking of generators, choose those carefully as well; the same EMF susceptibility applies. There are a few smaller diesel generators on the market (made in China, of course).
For a newer car, the same would go for the "box". Might not hurt to pick up a spare "electronic control module" at the junkyard (try it out to make sure it works!), and then keep it wrapped in foil. (Likwise with the spark coil(s), and, if your car has fuel injection, spare injectors, in the event that the solenoids driving them get fried).
Other "wouldn't hurt to keep on hand" spares would be the alternator, voltage regulator, starter (and starter solenoid, and, if used in your vehicle, starter relay), electric fuel pump, fan blower motor (never underestimate the value of heating and windshield defrosting in cold weather!), and, wiper motor. Then, things like lights (and, for the headlights, the headlight relay).
Another consideration would be sparkplug wires. Resistor wire could end up as a hollow "smoked" capilary tube, as the carbon resistance/conductor was vaporized.
The more modern the vehicle, the more "electronicified" it is, the more components there are that would be subject to failure, i.e., if some critical sensors are fried (i.e., the crankshaft position sensor), you are dead in the water, even IF the main computer and everything else is OK (or, in lieu of "OK", is replaced with a "tinfoiled" spare.)
Depending on your proximity to an EMP (and the strength of the event), some or all of those components could fry. The first to go would of course be semiconductors -- but remember, your alternator has several diodes in it -- and your voltage regulator is also comprised of semiconductor components (unless it's a circa 1960's/70's or earlier dual-relay type -- which would fail with a stronger EMP).
With enough of a "pulse", even heavy-gauge magnet-wire devices like starter motors could fail (even if the damage "only" consisted of heavily arced commutators).