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Try this first. Disconnect the battery. Hold your foot on the brake pedal for 1 min. Clean and reconnect battery. Now test operation to see if the red key light is off.
If the light is still on, insert each key into the ignition and start the car using each key. Now try the push button start system.
If this does NOT work, let me know with a reply and I will give you the next diagnosisi steps.ThanksDrew