From what you wrote, it would appear that you have purchased download files from Adobe for Premiere Elements 11 and a serial number specific to that purchase. At that time, to what computer operating system did you download and install that purchased download and its serial number?
What are you dealing with...activation of a Premiere Elements 11 program that was deactivated and left installed on your computer? Or some other scenario? Please explain.
I would like to rule out that you are somehow trying to use a Premiere Elements 11 Windows serial number in a Premiere Elements 11 Mac setup or the other way around.
Typically Adobe does not support anything put the current version 12. But, it might might the exception for Activation issues, not sure in this case. To find out, click on the following link, and, when it opens, navigate to the section on "Serial Number and Redemption Codes". It looks like the paths to Adobe Chat have shifted, and I need to figure out what it has done. But, for now, I think the path indicated should bring answers.
Please let us know the outcome.