I'm not sure which Core Services you are specifically looking for, but for several of them you can fill out the following form to get them provisioned for your organization: https://www.adobe.com/go/audiences
Following up on this issue. As its not clear of what Core Services you need access to? If you are looking for connection between Analytics, Audience Manager and Target then use the client that Cjensen provided. If there is a question on the access for getting into tools let me know what you are getting via a screen shot and we can try to help you resolve it.
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