Security light stays on

2002 Grand Prix GTP 3.8 L milage 90,000

Earlier in the week the key wouldn't come out of the ignition as it would not cycle back to the off position. After reading some other posts, found the solenoid in the steering column and was able to get that to work. However, the car would then start and die after 3-5 seconds. A repair shop found a bad wire and repaired that, the car runs fine, but the security light is on all the time now.
Can I get this to turn off and will there be any damage if it does not?