I know this is about 4 years late to help with your issue but just in case anybody else is having this issue:
My 2003 Buick Century is doing the same thing. All the lights, radio, power seats/locks/windows and all worked fine. Car wouldn't crank, just a slow click and security light is on. At first I did this http://www.youtube.com/watch?v=UWfvEouMMtcand
it fixed the problem but a few months later the problem came back and this time just jiggling the wires didn't help. Was told it would be $1100.00 to replace the VATS security system in the car.
Friday, July 26th, 2013 AT 12:00 AM