My purpose here is not to defend the book.
But, if you read it, you'll find mechanics have some success getting older cars without all the electronics to run.
The family of Matherson's late wife are small-scale car collectors who happen to own a 1959 Edsel, in addition to a Mustang. The two cars are so old that the EMP did not affect them because they have no modern EMP-sensitive electronics, such as transistors. Another local resident owns a vintage airplane that later becomes very useful, as it too is so old that it has no vulnerable electronics.
Source.