My money is on connector that ties ignition switch wiring as it exits column to dash wiring harness loom. Simple to check out at with a test light at starter relay as ignition switch Is turned to 'start' position. There are 6 main wires in this connector,,,one of which feeds current from ignition switch to starter at the underhood relay.

Male pins or female receptacles often lose their required snug fit at this connector.

Remote possibility that ignition switch itself is bad.

Can also test by running jumper wire from battery positive to the wire tab at relay that sends signal to starter solenoid. If cranks, either above connector is bad or firewall connector is.

If no crank, is solenoid or starter itself.

Doubt very much that a defective battery would cause zero starter response if headlights illuminate ok.