Need Advice on 2001 security light problem

My wife has a 2001 Impala that is acting strange. When she starts there is a clicking sound like a relay for a couple seconds then the security light comes on. After a couple restarts it stops, but it is getting worse. I am an aircraft mechanic and have rebuilt several older muscle car engines. Unfortunately, I haven't kept up with all of the newer electronic stuff. She took it to the dealer and they were baffled and could not fix it, so it looks like I'm on my own. I do have extensive electronic troubleshooting expierence and a few meters, but no auto computers equip.

can any mechanics steer me in the right direction? Please spell out the acronyms the first time. Thanks.