When I've encountered this very problem in the past I have merely emailed the publisher (Adobe in your case) explaining the situation and they have each time understood and re-enabled the serial number. The reason, of course, that software makers do this is to try to prevent piracy - you selling or sharing copied software and serial numbers to another person. But if you just tell them, I'm confident they'll help you. They want your future business. Here is the support page for Adobe (you'll select Premiere Elements from a list):

http://helpx.adobe.com/contact/

Good luck!