My 2001 Impala will not start at random times. That is, nothing happens when you turn they key except the dashboard lights come on. Sometimes it will start again after waiting 10 to 30 minutes. Sometimes holding the ignition key on while turning the steering wheel works. The problem most often occurs when there’s a sharp turn just before the car is turned off - like pulling into a parking space. It also occurs occasionally overnight. I also see the Security light come on at random times, but the two phenomena don’t usually occur in sequence.
With it working sometimes while turning the steering wheel, I’m going to guess a problem with the ignition lock cylinder, or the wires attached to it. Perhaps they have chafed through and are grounding out, but then turning the wheel straightens them out temporarily.