Word press is free cms system. As far i am concern, it doesn't needs any api key. But if you install any third party plugin like analytics or seo pack then it may cause some issues if they need an API key to be functional. So if you have any such plugin, then uninstall them and try again.
it could be in akismet or any other plugin. check which plugin installed is not working and requires api key, acquire one and it will resolve your problem.
Wrong thread this should go to web development, deactivate, activate plugins and watch it, when it goes then that's the plugin require input. oh and good luck, it works! that thing.
This message is of Pingler wordpress plugin. It pings 5 post a day for free, for more buy their API key. This is why message coming.