I understand that you want to know how to remove the information about your "old" Slingbox from your account.
You only need to visit accounts.slingbox.com, log in to your account and access the panel located on the left hand side of the screen. There, make sure to select "Slingbox Directory". Right there, you will see your Slingbox units listed. Select the right one and click on the "Remove" button on the right hand side. This way, you will be able to get rid of the old Slingbox information.
Hope this helps!