The module has a basic timing map built into it and will fire the plugs even if there's a faulty connection between it and the ECM, however, the ECM must see the EST pulses before it will fire the injectors.
I think I've covered this in previous threads, but here are some simple tests. First, get a trouble light, connect the clip to ground and probe the Fuel Pump Terminal in the ALDL connector:
Now, turn the key on but don't crank. Does the light come on for around two seconds then go off? If so then the ECM is working fine as far as it having power and responding. Next, unplug the oil pressure sender and try cranking the engine. Does the test light come on? If so, that means the ECM is seeing EST pulses from the distributor module. If the test light comes on when first turning the key to RUN before cranking, but does not come on when cranking, that tells me the ECM isn't seeing the distributor module for some reason.
If all of the above tests are successful, connect the test light to power and probe a known ground to verify the light works. Next, probe the two wires at the ECM that feed the fuel injectors, per this schematic:
When probing each wire at the terminal, crank the motor. The ECM works by providing ground for the injector coils, the other side of the injectors are connected straight to full time power via the ignition switch. If the light blinks on and off while cranking it means the ECM side of the injector circuit is working fine. If not, and the ECM otherwise is working and runs the fuel pump when cranking then the ECM has got problems internally.
Once you verify the ECM is working then use the test light connected to power to probe the injector harness connector by the thermostat for pulses. If you get pulses at the ECM but not at the connector (probe the correct wires per the schematic) then the harness has a problem. If it blinks at the harness then you connect the test light to ground and probe the other wires in the harness connector. If you have power there then the problem is in the injector harness under the manifold plenum.
It's really a simple circuit, not to terribly difficult to troubleshoot with just a test light.
JazzMan