Hello Alf
I have been through the won't start for no reason issue. Its a PIA. Assuming the security sys is the same in a 1991 here's what I found.
Look for the simplest thing first, blown fuses maybe. There is lots of info on line.
If its the security system, you will not hear the fuel pump nor will the car turn over, but you will have power every where else.
There are relays associated with both the starter and the fuel pump that should be checked.
There is info on line that explains the various conditions related to the "security " light that it might point you somewhere.
It could be the chip in your key, I see you tried another key but did you try it immediately ?
Try a start, if no go, wait at least 10 minutes. If you repeatedly toggle the starter the system thinks its a theft attempt and can shut down,
I tried a cheap VATS by pass from Mid america, it seemed to work for a while but the problem re occured.
I had the ignition cylinder replaced, that seemed to work for a while, but problem reoccured.
I installed a "New Rockies" module that completely by passes all of the security systems not just the keys and it worked for about 2 years then bingo, a no start happened again, at which point I by passed the starter safety switch on the clutch pedal.
It has started ever since, which, I hate to say for fear of jinxing the whole deal.
Hope you find something simple, good luck.