Are you using a factory Saturn key? IMPT:

When there are PASSLOCK issues, the BCM can be blamed, but there is a sensor in the ignition switch that can also go bad. It is part of the Passlock System. The voltage it sends to the BCM is that "password" I mentioned earlier.
I suppose it is within the realm of possibilities that the PASSLOCK sensor in the ignition switch has failed. Usually, they act up for a while, falsely triggering security, but can be reset by the 30 min relearn.
However, if the ignition cylinder receives the initial V from the BCM, but never sends back the "response" voltage (the Password the BCM is expecting to receive, which must match what is stored in the BCM), then security will be triggered, and by definition, it is impossible to do a PASSLOCK II relearn because the ign cyl and the BCM aren't communicating.

I'm sure there is a way to test for whether this sensor is bad maybe by finding out the pinout for the BCM and checking for V on the return line from the ign switch. This will detect a completely dead passlock sensor, but if it is putting out any V (current) at all, you don't know if it's at the right level. Although if the BCM and ign switch were communicating, you'd think they would just agree on the return sig voltage during the relearn. But yours will not do so, so it's either the BCM or the ign switch sensor. Maybe there is a youtube video on figuring out which one it is.. There are zillions of bypass kits for PASSLOCK II -- all they do is insert themselves into the system--they don't really bypass anything. They remove the (key+sensor) signal and replace it with a voltage output that keeps the BCM happy.

Sounds like you tube time.
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As for weak spark or no spark:

This test is best done in the dark
-- pull the plug wires off the coils (LABEL THEM) and have a friend crank while you watch the coil towers
--you should see an arc across each coil, with the arcs alternating between the coils. Do you? Is it strong, weak, or non-existent?
--if weak or non-existent, hook up jumper style to a running vehicle and repeat the test. Stronger spark?

There are other things to check but this is a basic coil operation check. Chances are if the coils are not damaged, the very pricey DIS Ign module below them is ok. If not, then we have to determine why it is weak or non-existent.

Basically, you can find out whether the ign switch PASSLOCK II sensor is bad or key is bad by measuring the resistance of your key, substituting resistor or resistors in series (that match the resistance of your key) in place of the feed to the bcm from the column, doing the relearn and seeing if the ign sensor is bad. Apparently, the resistor in the key can go bad too. Basically, you're simulating the key and sensor resistance. In doing so, you're bypassing the key sensor but not the rest of the system (BCM).

Sample .youtube video for a GM --- check your wiring diagrams.for the correct wires, I think a 10% tolerance is ok but getting it within 5% your reading would eliminate doubt.

Also I have seen folks state that when you measure the resistance of the key, you need to do so in both directions. THere must be something besides a resistor in there. You want the higher of the 2 readings 500 ohms to 10Kohms is expected.



NOTE: the vid was for a 96 vette which apparently still had the right "password" in the BCM so his started right up.
Yours likely will not, so of course.....................perform another relearn..

Hopefully, it starts or at least fires, and the injectors are opened.
If it doesn't start, check your resistances and wires

If the fuel pump relay is still not closing, still might be a bcm issue;
.
***Have you checked the back side of the panel where the fuel relay plugs in to ensure there are no broken wires or melted contacts?"""" And have you confirmed continuity from the relay input to the BCM***

So I ordered a used BCM & PCM from the same car, but unfortunately they arrived the day I left the country for awhile.
So now they are sitting with my lazy stoner friend, so not sure if/when he will follow the instructions I left him to try & get the car up and going again.

I'll update here if he gets his lazy self up and tries anything!