The ECU tells the fuel pump to run, so it doesn't seem likely that's your trouble, though possible. To check the cam sensor depth, if you have no tools, hold the new and old ones up to each other so the end of each touches the flange of each. They will probably be identical so you can assume the shims that worked in the past will work with the new sensor. The shims are more likely to be dependent on individual case machining than difference in sensor length. Since you're already installed it, if the shims are in, ok. If you installed it without shims, pull to see if the reluctor has shaved the tip of the sensor.
The schematic I have shows that the sensor is a simple analog coil, the third wire is in fact a grounded shield to keep AC voltage from messing with other electronics. The wires on the ECU side of the sensor connector should be tan and white, pins 7 and 12 on the ECU connector. With a second helper and a digital multimeter, you can test the sensor at both plugs for AC voltage output while you crank the motor.
The coils are powered along with the fuel pump and injectors by the fuel pump relay. Fuel pump primes...Yes? pull an intake boot back, open the throttle and look with a flashlight into the open throttle body. When you first turn the key, or perhaps the run switch, the injectors should spray for a moment, to prime the engine. If you can confirm that you have fuel from the injectors and signal from the cam sensor, then we can look at the magic box. Until then, I'm with Dr. House; "It's never the ECU".