Correction, GM does not fire the spark or the injectors until it has had 1 crank and 1 cam puls. If either one is bad the engine will not fire. Besides that, you are correct. Without a scanner you will need a good DVOM, back probe the signal wire for the puls to the ECM turn over the engine….. Do you get 5 volts?
You can check the cam sensor by pulling it out back probing the signal wire and passing a magnet past the sensor face. Does the VOM jump? If they work that much it should be just enough to fire.
Why did you change the ICM? You may want to check for bent pins in the plug. Did you replace it with a used piece?
Start out old school; are all fuses good? Etc etc etc