Cancel all active resources and cancel account.

You might be seeing the new AWS Billing page layout, and your right it doesn't have a section called "Details" In the new experience about halfway down the page you will see a tab called "Charges by Service".

If you don't see any changes here, you should be good to close your account.

If you see the blue bar in your console like the screenshot above you can go back to the old bills page console that will line up with the instructions your following here

Note: The Billing and Cost Management console takes about 24 hours to update usage and charge information for active resources so as long as you haven't been using the account in the last 24 hours you should be fine.

Thanks so much - that was very helpful indeed. No charges as I suspected, so I'll go ahead with cancelling the account.