Solid State circuitry is most prone to EMP. EMPs induce voltage fields that will blow the junction of most solid state devices unless the field can be effectively shunted to ground. Grounded cases don't work, because the field raises the ambient electrical environment and tends to cause a lot of eddy current activity on chassis and in suspended cables. Lightning generates an EMP, though not to the level obtained by airbursting nuclear weapons.

In short, if you are within the range of an effective EMP burst, you can say goodbye to anything electronic. Even assuming an old beater vehicle, you are going to lose the alternator because the diodes and the regulator are all semi-conductor solid state devices. A diesel can maybe keep running, but it must be completely mechanically based (including the injection controls) and none of the other electronic stuff on the vehicle will be funtional.

Coils can be nearly as vulnerable. A coil microphone element will probably eat itself, as will a tape recording/playback head.

Engine coils will likely take the juice, as will big speaker coils, but small engine windings may or may not make it, like that electric shaver, or the dremel tool, etc.