Looks like in version 3 you need to pass the ClientID in the URL and not a key as you do in the free version: https://developers.google.com/maps/articles/v2tov3#newkey
So your URL should look like: http://maps.googleapis.com/maps/api/geocode/json?client=xxxxx&address=Dallas&sensor=false
Not lucky enough to have a paid account so I cannot test - but I think that will get you on the correct path.
Relevant from this link: https://developers.google.com/maps/documentation/business/webservices/
Client ID
You must include your client ID in all API requests. Your client ID
identifies you as a Maps API for Business customer and enables support
and purchased quota for your application. Requests made without a
client ID are not eligible for Maps API for Business benefits.
If you're switching from the free API services to a Maps API for
Business implementation, you must remove the key parameter from your
requests. Google Maps API web services will deny requests made with
both a client ID and a key.
More information is available in the Authentication and Authorization
chapter of this guide.
If you have lost your client ID, you can recover it by logging in to
the support portal and clicking Maps: Add URLs from the links on the
left of the page.
EDIT
For more information, including instructions on passing your client ID to the Earth API, v2 API, and the Maps API for Flash, please read Loading Client-side APIs.
If you have lost your client ID or cryptographic key, you can recover them by logging in to the support portal and clicking Maps: Add URLs from the links on the left of the page.
Best Answer
Read this tutorial, it's very helpful...hopefully it helps you out