is there no way to remove a device you no longer have access to?

PC Crashed totally. New drives and new install of OS. Now its still showing as an associated device and I can't remove it. Nor can I use the new repaired PC because I have too many associations?

And also, isn't this STUPID? If the idea is to have Apple seamlessly in a family unit, does it occur to this behemoth of a company that we have iPhones, ipods, ipads, and computers? I have more than 10 devices just myself!