Sounds like the data buss wire from the ECM to the ALDL connector might be bad, or not making contact at one end or the other. That would be supported by the new ECM you tried also having connectivity issues with the scan tool. Even if that's the case, the check engine light trick should work on your '96. I found one site saying that for the '96-97 you need 4 cycles, not 3. (on-off-on-off-on-off-on) It may take a bit of time for the light to start flashing according to some of the sources, so give it 20 seconds or so after the final "on". If you cycle the key too fast or too slow, I don't think it'll work either. About a half second or so in each position, like you're reading it s-l-o-w.
Here's a youtube clip that starts just after the last "on". You can watch the Maint Req and CEL both clear, then it flashes the codes. 12, 72, 55.
To approach it from another angle, if you unplug the ECM or disconnect the battery to clear codes, does the light come on right away when you start the engine, or after the engine has been running for a few minutes, or only after several drive cycles?? That alone can tell you what sort of problem you're looking for. Several drive cycle problems are generally emissions related, and I'd suggest looking at oxygen sensors or perhaps for a plugged cat. Immediate on lights are shorted or open sensor inputs, and you could check wiring to sensors.
Good luck!