I suspect that you are not going to get any support from Adobe on this since you are not using the latest version which is Premiere Elements 13.
You can try the link John as posted; it is worth a try.
If you get sent back to "Ask the Community", that is us (user to user), please give more details and we will try to figure out the
cause of the situation.
My first question would be "If the installation is accepting the serial number, where are you when you get the message about the Invalid Serial Number?
Without going into specifics and do not post serial numbers, did you purchase the product from Adobe direct or an authorized retailer or a private seller?
Are you working with a regular version or one of those Student Teacher versions? On what computer operating system are you trying to run Premiere Elements 13?
We will be looking forward to your progress.