You can't install D3: ROS Standard edition over D3 Starter Edition. You must have D3 Standard Edition first before you can install D3: ROS.

Did you uninstall your copy of Diablo 3 in your computer? Some old data with regard to the starter edition may still be on your computer.
It's not possible that even with a new bnet account, you still can't activate the D3 standard edition unless the serial key has been compromised.

Anyway just want to be sure: Do your have BOTH the D3 Standard Edition and D3:ROS Standard Edition?

Bnet account refers to your online account with Blizzard. It do not reside in your PC.
If you have create a new bnet account with new ID and password, your old D3 starter edition shouldn't exist in your new bnet account.

When you key in the your serial number, key in exactly as shown including the "dash" (-) and in capital.

If still fail, you have to refer to Bnet customer support for help or there is a possibility that your serial key have been compromised.