Give this a shot and good luck:
Link to Activation Key Generator
If you get a new activation key, go to the XP Start menu and under Hollywood FX open the Easy FX Editor and under help you will see a section to enter the activation key. This is not the serial number. You will need that also and the Passport number from the Liquid About screen in the Liquid Help menu.
You will need the email address that the original owner used when he registered the product. The link to change the email address is broken. If you are successful, the new key will be shown on screen and not emailed despite what the screen says.
As Pinnacle is now owned by Corel and Liquid has been discontinued for many years there is no one I know to contact so if this does not work, or you cannot get the original email address, you are probably out of luck.
Again, good luck.