2001 Impala Intermittently Won't Start

My 2001 Impala intermittently will not start. Approximately one in every 40 starts, my starter does not respond to turning the key. Though my starter does not respond, my dashboard does energize when the ignition is turned on. After I wait for approximately 10 minutes, the car starts. I have the impala LS with the security system. This sure appears to be an intermittent electrical problem (security system?). I have a good battery with a good alternator. Any suggestions?

in 2001 is the BCM in control of the starter solenoid like on my 03? if it is I would have to ponder the possibility that the BCM is flaky. But there is so much other stuff that could cause it. Like the nuetral safety switch or a bad starter. Or even that security system, although I think that just stops the fuel pump so cranking shouldn't be affected?