1991 Cadillac Seville starting problem

Most probable is a failed ignition cylinder. The wires that carry the key resistance value to the module eventually break at the cylinder. Try a second key if you have one, otherwise the lower column panels will need removed to access the wiring(two small white wires inside an orange sleeve). Some vehicles, this wiring had a two wire connector that made it easy to measure the resistance, other vehicles these wires were part of a large connector. If you can locate them, seperate the connector and measure the resistance across them with the key in all ranges. If all are open, you will need a cylinder and new keys.