Are you talking about this plugin?
https://www.ads-software.com/support/plugin/songkick-concerts-and-festivals
If so, please post to the support forum there. I found your question just by chance.
You only need an API key if your website is commercial. Please read the API terms of use for the definition:
https://www.songkick.com/developer/api-terms-of-use
I just released a new version that should clear all the warnings.
However, the reason your plugin is blank might not be that. For the plugin to work, you need to setup the widget with the information about the events you want to be displayed. You can set them in the admin page, when you drag a widget to the area you want it to be, there’s a form you must fill in. Please check the readme for examples, and ask if you have any questions.