If your API Key appears not to be working and you are not sure if it is a problem with your site, or your shortcode, or the plugin, it is simple to check directly with Eventbrite.

Just go to
https://www.eventbriteapi.com/v3/users/me/organizations

and put your Private key into the OAuth token field.

If it says it is invalid, then you are best to double check and create a new one following the instructions here.