Impalas of 2001-2003 vintage have a recognized problem of randomly not starting. That is, turning the key lights the dash lights, but nothing else happens. Leaving the car alone for a period of from 10 minutes to 30 minutes sometimes solves the problem, as does twisting the steering wheel while holding the ignition key to "Start." I've seen lot's of speculation (mostly involving after-market security systems) but no real answers. As far as I know, mine does not have an after-market security system.