Lol thats exactly how they work.
No power = no run. Modern day, with the exception of simple (definitely not military-grade) engines that rely on a mechanical distributor instead of a set of sensors and a ECM, everything you're going to find in both gasoline and diesel engines has a computer or multiple computers that are necessary for the basic function of "running". And that doesn't include other stuff like the gauges, automatic transmission behavior, every other system on the vehicle, each of which likely has its own dedicated computer module. Modern stuff has computers everywhere, so unless this is a 1953 M38A2 or such like, an EMP will definitely kill it. At least until a knowledgeable-enough mechanic gets ahold of it.