Not an expert so somebody should hopefully chime in but you’ll need to deactivate your license on the old box, also make sure you know what the license key is, if not then if you through the motions of logging a call it will generate an email template text that should hopefully have your license key.
Within settings there is also an option to export settings to a file, so make sure you do this. I’d also take an export of the BI registry key as a secondary backup.
Then install BI on your new box, activate it using the license key and then within settings import your previously saved settings file.
If your config is not too complex then some suggest reconfiguring from scratch but only you can decide if thats an option or not.