Try installing Cadence Desktop on your new PC and using the serial number that you already have to register it. Unfortunately, the application has been discontinued, so if reusing the same serial number doesn't work, you won't be able to purchase Cadence Desktop again even if you wanted to. Furthermore, the tool's official website is no longer functional, so there's no way for you to contact the developers either to see if they can help you out.
Alternatively, you can try looking into an application like beaTunes, which offers pretty much the same functionality.
