What version of Premiere Elements do you have and on what computer operating system is it running.
Typically, for more recent versions, you would go to the opened project and Help Menu/Deactivate. Close out of the project. And, then you would uninstall via the classical Control Panel route.
You might also find a deactivate option to check in the course of the uninstall. But I would make sure to do the one in the opened project nonetheless as well as any deactivate in the uninstall dialogs.
Please let us know if the above answered your question.
You are allowed the same purchased serial number on two of your computers. So, I would ask, are you talking about a second computer here or a third?