Intermittent no-start

I’ve got an ‘07 Silverado HD (new body style - basically an ‘08) with duramax and almost a half million miles. Recently I turned the key and it failed to start. No attempted. Radio and everything came on, but no starter. I replaced both batteries and it started. A few days later it did it again. I replaced the starter and it started. Then a few days later it did it again.

Any other ideas? Ignition switch in the steering column??