The Explorer documentation says that it uses it's own quota (and key) to make requests, not yours: https://developers.google.com/explorer-help/
This means that most probably it was a glitch or a bug in Explorer and not your engine (it seems to be working fine for me now). Try to issue request from your application with your API key and the problem should be resolved.
If you just want to try to issue a single request without writing code you can use Postman Chrome Extension: https://chrome.google.com/webstore/detail/postman-rest-client/fdmmgilgnpjigdojojpjoooidkmcomcm?hl=en