Both Win-97 and Win-500 show you the installed license key when you run the program using Help; License Key menu options. Much easier than searching the registry. Now both assume that you can still run your old PC. One other option might be to search through your old emails where you received your license key. The purchase screen stated to save the information in a safe place since you'd need it to reinstall the software on a new PC or after a hardware failure. It also states that the company wouldn't be able to send you a replacement key.
Be aware that you not only need the issued key, but also the name as sent in the registration e-mail. This name includes several fields and must be entered exactly as sent. The name as issued also appears on the license key dialog box so if you can run the software on your old PC, you should have everything you need, even if you can't find the original email sent to you with your registration information.