With a Retail, not a OEM, license, you should be able to unregistered Windows 8.1 and then use your original key to install on the new system.
Warning: Do the below at your own risk.
General Steps
- Make sure you have your original product key and install media first. If you cannot find your key, try using Magical Jelly Bean Keyfinder
- Deactivate your Windows 8.1 product key, by launching a Command Prompt As an Administrator and type in the following command:
slmgr.vbs /upk
or if that does not work tryslmgr.vbs -upk
. - Once done you can activate the new computer after install.
Note: Don't forget to put the key sticker on the new device.