Get a multimeter and check for voltage and continuity. Continuity is checking a bus or wire for 0.0 resistance.

Unplug the wire harness for the ECU and check for voltage with the key tuned to "ON". Find the pin that has power coming into the ECU and see if it reads 12v check from this pin to ground, NOT the ground pin but chassis ground (from the power pin to a bolt on the frame).

If it does not read 12v check your battery to see what the voltage is across the battery terminals. What every is at the battery should be the same from the pin to the chassis.
If the power reads lower at the pin than it does at the battery then you have a bad wire. all the voltage cannot reach the ecu.

if all is good so far check the positive 12v pin to the ground pin. then check the ground pin to the positive battery terminal. All these readings should be the same.
Now check the ground pin to the ground chassis for continuity you should get 0.0 resistance check a few different spot on the car to make sure you get 0.0 resistance. Rust oil and other thing could show resistance on the meter.

Let us know how it goes. Come back for questions and updates.