The ignition control module is different for a manual transmission and an automatic. One has provision for push starting.
The module also controls amperage to the coil, giving more in START than in RUN. If the module is cooked, it might enable spark in START, and cut it off in RUN. The module produces a signal that the computer uses to know the engine is running in some years, and will enable the fuel pump again after the initial 3-5 second run to pressurize the system.
Be sure you have the correct module, and that your ignition switch on the column is in good shape. Mine seemed to disconnect power to the ignition when released from START, and the engine died intermittently...
tom