Highly doubt the switch is bad. It's not like a switch from a 97-03. 04+ use a low amperage style switch. BCM must be programmed with a tech2. They CANNOT be used as they are locked after a few ignition cycles. Symptoms of a bad bcm are no Interior lights,security not enabling starter, locking issues, radio not powering on or locked, no communication with the bcm. Check your power and grounds at the unit other than that sounds text book bad bcm
Jumping your starter will prove nothing other than the starter motor itself is fine. The car will still not run
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