1998 Chevy Malibu starts then shuts down

I understand. However, the initial problem was not addressed by the new cylinder. When I inserted the cylinder and key I started the car as directed, it died, as supposed to, then I waited the 10 minutes for the security light to go out, but it doesn't go out no matter how long you waited. It's still not recognizing the key is inserted and turning on the interior lights or buzzers. So I need to know what specific part controls that switching on. Body control module? Powertrain control module? Or a simple relay somewhere? I'm hoping once that connection is fixed, it will recognize the key and allow me to program it as directed. My friend I purchased the car from owns several and has replaced the cylinders and they run the security program automatically in 10 minutes.