The trial license is a fully-featured time limited trial. The REST API should definitely work as long as all of the steps are followed as per the documentation.
Are you definitely querying with the right URL? There are examples here. The REST API is available from the admin website address, not the MVC presentation website, so ensure you're using the right domain or port number. The format of the URL should be
I personally don't use the REST API that often, and prefer to create custom web API controllers in the presentation website.