When the aliens first appear and cause an EMP (Electro Magenetic Pulse), all the cars stop working.

1. An EMP would not disable an old carby-and-distributor type engine. (much like the one the main characters son steals), it would however disable the newer EFI vehicles' ECU(much like the minivan they steal).

2. An EMP would not disable a solenoid. A solenoid is essentially a coil of wire, that when energised, creates a magnetic field and draws in a plunger.

3. Replacing the starter solenoid will not get a car running again. If the EMP DOES disable solenoids, replacing the starter solenoid will not get a car running again. There are many solenoids or similarly operated devices in any given vehicle.