It is my understanding over the years that the Premiere Elements 3 "unlock activation" is not the same as the serial number and must be gotten from Adobe.
So, I do not believe that those Lost Information and Lost Serial Number links are going to get you anywhere. But let us see.
By any chance did you put the Premiere Elements 3 "unlock activation code" obtained originally in a place for safe keeping?
Even though you do not have the current version which Adobe typically will only support, I would contact Adobe via its Adobe Chat for help on this matter.
Please click on the following link
Adobe ID and Signing In
Adobe ID, sign in, account help
If the link does not hold its set, then you will need to navigate to the Chat Panel using the above titles as guides.
Please let us know the outcome.