Not sure if that helps or not to answer your question but I know it doesn't address that you stuck at a point and you need access to the 2013 version. In addition the free educational license is only allowed for the current release (2018) and three (3) legacy versions (2015-2017). Overseas the rules are a little more relax due to other country/government laws. No one here in the states can get this version anymore not even students/schools.
The 2013 version was retired 2 years ago and no longer supported by Autodesk. In the end you have to accept these guidelines or not. We the users of Autodesk products have no control or say in this matter. However when it comes to the free software that Autodesk provides to students and schools/college, certain rules/guidelines come along with it and there's no exception.
I also fully understand that schools, companies, and/or individuals may not have a budget, finance, or the money to upgrade their hardware and software. Solution Product keys are required for installation of Autodesk products and are. That you want to teach students an Autodesk product. Issue You want to know the product key for your Autodesk 2013 products.