There's only three possibilities here, if my thinking is correct:
1. Injector driver in the ECM (yes, the pulse comes from the ECM).
2. Wiring between the ECM and Injector.
3. The injector itself.
The noid light should still light up if the only problem is a bad injector - the noid light will flash as long as voltage is reaching it, regardless of whether the injector is good or bad (if I remember correctly). So, I think we can rule-out #3.
If you have a friend nearby with an ECM, see if you can swap it out with the one in your car. If the noid light starts firing after the swap, then you know your ECM has a bad injector driver. If the noid light still does not fire, then you know there is bad wire or connector somewhere between the ECM and noid light location.
It seems like injector wiring harnesses are not particularly robust on our cars, many people have to repair or replace them. So, I would guess that is most likely the problem.
Good Luck,