Move or reinstall QuickBooks Desktop to another computer - Intuit
Retrieve license/registration key from 2013 - QuickBooks - Intuit
This is where things get difficult because Intuit no longer supports version 2013. However, you are not completely helpless.
Please be aware that Intuit discontinues live support and services for older versions of QuickBooks. As of May 31, 2016, QuickBooks Pro 2013 is no longer supported. This means you will not be able to register the software automatically through the internet. If the online registration fails, you may be required to contact Intuit support directly to manually validate your ownership using your license number. Additionally, services like payroll and online banking will no longer function with this version.