You, didn't identify the year of your car, but the security system for the car is probably the GM Passlock system. I have a link for bypassing it, but that may not be what you want to do, and also, the link may not cover your system.
It is also possible there is a fuse, or fusible link blown for the ignition. Also wiggle the shift lever in case it is just the neutral safety switch acting up. Another possibility is the starter itself or the ignition switch. Be sure to check all these out before you fiddle with the security system.