Hello,
I'm not particularly familiar with the software you're using, however it seems the error message would appear if it fails to validate the API key it has with Google. I recommend checking a few things about your Google Developers Console API key:
- Translate API is enabled inside
API Manager for your project
- The API key is
set up correctly
- You're entering the exact API key when asked inside SDL Trados Studio
- You've retried generating the API key and allowed some time for the new key to be active
- Try using the API key elsewhere (another software or program) if possible
I hope that helps. Cheers!