When you uninstalled Premiere Elements 9.0/9.0.1 Windows from your computer, did you deactivate it before you uninstalled it? Deactivate is not the same as Uninstall. And, what counts to the Adobe count refers to the number of computers on which you have the same activated serial number. You are allowed 2, and you do not use the two at the same time.
To deactivate Premiere Elements 9.0/9.0.1, go to the Premiere Elements 9.0/9.0.1 Editor and its Help Menu/Deactivate and click on Deactivate. That is the key step. You do not have to uninstall the program at that time if you plan to come back to it again some time.
Please consider. Any questions or need clarification on the above, please do not hesitate to ask.