What causes the theft light to stay lit but still run on this 98 Olds Cutlass?

What is your question?

The key would not turn in the switch due to the tumbler cover being loose. I put a new switch in the car, proceeded to program the switch but the light never goes out. The car starts and runs without any problems. This is a car I am working on for a customer and I don't want her to have to worry about the light. What can I do?