Try to change the owner of Diagnostic Server service to your own domain user (instead of dedicated) and see if that makes a difference. If it does, it means that the domain user has permissions that the other one doesn't.
If the above does not help please run the following command:
netsh http add urlacl url=http://+:3166/ user=domain\user
An example:
netsh http add urlacl url= http://127.0.0.1:3166/ user=QPROD\tsmith
Run this command on the DS machine in a command window that is running as an administrator.
Replace domain\user with the Diagnostic Server service account owner details.
Then restart the DS service.