AWS Directory service admin does not have any privileges

It sounds very much to me like the computer account for the DC has been accidentally deleted. Do you think this is possible? If this is the only DC and you've not made many changes since this happened, you could boot into DSRM and log in using the restore password and try to restore the tombstoned objects, if there are any.

In order to not drive myself nuts I found the following, you should try to rtfw.

1. Click Start, click Run, type dsa.msc, and then click OK.
2. In the task pane, expand the domain node.
3. Locate and right-click the OU that you want to modify, and then click Delegate Control.
4. In the Delegation of Control Wizard, click Next.
5. Click Add to add a specific user or a specific group to the Selected users and groups list, and then click Next.
6. In the Tasks to Delegate page, click Create a custom task to delegate, and then click Next.
7. Click Only the following objects in the folder, and then from the list, click to select the Computer objects check box. Then, select the check boxes below the list, Create selected objects in this folder and Delete selected objects in this folder.
8. Click Next.
9. In the Permissions list, click to select the following check boxes:
   • Reset Password
   • Read and write Account Restrictions
   • Validated write to DNS host name
   • Validated write to service principal name
10. Click Next, and then click Finish.
11. Close the "Active Directory Users and Computers" MMC snap-in