'02 Regal starting issue

I have a periodic issue with the car not turning over, hot or cold. All other electronics work just fine, but when I turn the key, nothing. I will let it sit for 3-5 minutes, and sure enough, it will start right up. This happens about once a week. I have heard a faint 'click' while waiting for the time to come to start it, so I am thinking some electronic issue. ANYBODY else?????:banghead:
FYI...
--Clean/tight connections

Do you have the SECURITY light on or flashing?

If not check the 12 volts to the starter solenoid which comes from the cranking relay and ignition switch.