In the dialog that you are getting which appears to be one for the tryout with its typical Buy or Continue Trial, do you see a field that says license this product?
If you do, click on that and follow the instructions using your purchased serial number.
Reminder, you want to be using what is labelled "serial number" nothing else. Are you?
If the above idea does not work, then another plan is to download and install the tryout files for Premiere Elements 11 and insert your purchased serial number in it. But, read the Note: Very Important Instructions at the following web site otherwise you will get hit with Access Denied message.
The approach to contact Adobe can run into trouble if Adobe classes your call as one for troubleshooting rather than product activation. Typically it will not help unless you have purchased/registered/current version (12/12.1). It may just send you back to the Forum, but you could try, depending on how alternatives are working or not working for you.
Click on the following link, and, when it opens, click on the statement "I still need help" to bring up the Adobe Chat.
Please let us know the outcome.