Code P0513?

Have you tried the spare key? Also, you might want to disconnect the battery overnight to see if that helps. If not, I would call a mobile locksmith who can code a new key for you, as a last resort the BCM will need to be replaced.

The OBD-II code P0513 for a 2015 Chevrolet Silverado corresponds to the "Invalid SKIM Key" error. SKIM stands for Sentry Key Immobilizer Module, which is a security feature in your vehicle that helps prevent unauthorized starting of the engine. This code indicates a problem with the communication between the key and the SKIM module.

Here is how to change the BCM out, you can get a preprogrammed unit by searching Google or Ebay.