To many (most) of the sensors the ECM supplies a voltage lower than battery voltage. Typically 5 volts, but sometimes a little more. The sensors supplied are grouped (a sensor loop), anywhere from a couple to half dozen sensors.
Typically the Check Engine light you see when you initially turn the key to the run position, fails to light at all if a sensor is shorted. The check bulb at start stops functining. Which usually indicates a shored sensor or a partially shorted sensor. The ECM shuts down to protect itself.
When the Check Engine Light fails on my 96, I unplug sensors one at a time until the light (CEL) comes back on, when I turn the key (initially) to run. You remove the shorted or partially shorted sensor from the loop and often the ECM will function again.
Someplace to start, unlikely to help if the wiring is shorted, the power to the ECM is flaky or a ground is bad.
Usually when an alternator fails the voltage regulator part of the ECM will fail, it seldom affects the rest of the ECM functions. The exception being reversed polarity at the battery or a serious voltage spike.
Low voltage is usually temporary and doesn't hurt anything long term.
Don't confuse an ASD relay issue with a sensor or ECM issue. I found a flacky connection under the dash near the gas pedal that would sporadically de-energize my ASD.
Just some ideas.