If your computer system uses a router, please turn it off for about 30 seconds and then back on.
Also, turn off your antivirus and firewalls.
Try the Validate again, do you get the Serial Number Validation message again when you reopen Premiere Elements 12?
You could also review the following
If all else fails, then please contact Adobe via its Adobe Chat to discuss "Serial Number Issues or Activating My Product". To do that, click on the following link. When it opens, click on the question "Still Need Help? Contact Us." to bring up the Adobe Chat to discuss the "Serial Number Issues or Activating My Product" topic.
Please let us know the outcome.