The service manual says the "SECURITY" lamp should illuminate for 5 seconds when the ignition is first turned on, if they system is OK. If it stays on or flashes, there is a problem.
Also, if the system senses an incorrect key resistance when attempting to start, starting (including fuel) is disabled for about 3 minutes.
A defective Tranmission Position Switch (TPS) or adjustment, could also prevent starting.
On my 95 Cutlass Supreme, the back-up lights stayed ON when the car was OFF. I had to remove the fuse (and then my electric trunk release wouldn't work). After a bit, I put the fuse back in and now the back-up lights didn't come on anymore. I assume it's the TPS or wiring. I haven't replaced the TPS yet!