The most common reason that will cause this problem is an API key that is not linked with a valid billing account.
Have you also enabled billing on Google? Although they provide free credits, this must be done in order to work.
Access Google API Console Here: https://console.cloud.google.com/
Also please see from video tutorials and PDF guide that there are two APIs you must enable.
(Google Maps Javascript API and Places API)
If you have CitationOptimiser, please follow this PDF guide too. There is another service you must enable on Google API.
(THIS IS ONLY FOR CitationOptimiser Module)