2003 Buick Regal Help please! Possible Ignition Problem

My car started acting up when I turned on the left turnn signal. It would die but only if the car was cold. Than shortly after the lights on the dash would flash on and off continously when key was in ignition. Now the car won't start at all. There is absolutely nothing when you turn the key to start. No noise, no click no nothing. It still flashes though. The flashing will stop when you turn on the headlights. We have checked the starter, battery, battery cables, battey posts, alternator, relays, fuses, fuel system. Everything is fine. I have been told that it is the computer chip in our car keys. That the anti theft system is armed because the chip in both our keys went bad and that the entre car needs to be re-keyed. A very expensive and dealer only job. I think it has something to do with the electronic switch in the ignition. I am not sure what it is called though. Could someone please help me with this problem. I am at my wits end.