The T-Bird's ignition is timed a solid-state electronic ignition control module that reads the timing from a sensor and grounds the coil causing the high-voltage burst of electricity that fires the spark plug. The role of the distributor is to select which spark plug should spark. Prior to the invention of electronic ignition, gasoline engines used a set of mechanical points that rode on a cam lobe under the distributor. When it came time to fire a spark plug, the points would come in to contact with each other and cause the coil to ground. This is the system used by the '68 Plymouth.
All fuel injectors for gasoline-powered road cars (mechanical injectors were used in racing for a while and were used for many years in diesel engines) are controlled by an ECU. Early Bosch fuel injection units used in 1960s VWs used an ECU the size of a small suitcase. When EFI became more mainstream in the mid '80s the ECU was significantly smaller. They weren't nearly as complicated as modern ECUs--they just ran a loop reading a few sensors and adjusting fuel injector speed and duration.
Starting the engine has been pretty much the same since electric start came out in the early 1920s if not earlier. A big relay (or in really old stuff a big switch) sends lots of amps to a powerful electric motor that turns the engine over. Even if the motor did get fried by an EMP, the '68 plymouth likely has a manual transmission and could be roll started.
For the record, your '84 T-Bird was a piece of shit. So was my '84 Mercury Cougar