If you can't log in to
https://registrationcenter.intel.com with the information you have, the companion forum on registration and licensing should be able to help you. You can submit full license ID information in a private post there.
Once you have logged into your account, you can obtain a fresh copy of your license by email, and download compiler versions issued during the one year term of your license.
There's no formality involved in removing a computer from service and installing the compiler again. If you have a floating license, that is attached to a specific license server, and you can get it changed by a private request on the licensing forum.
