no problem, just re-install pse 9 onto your new computer and activate with your serial number.
if you no longer need the original pse 9 installation, deactivate it (help>deactivate) and then uninstall it.
if you need the installation file for pse 9 and if you follow all 7 steps, you can dl a trial via one of the links on this page: http://prodesigntools.com/photoshop-elements-9-premiere-elements-9-direct-download-links.html
and activate with your serial number.
if you have a dl problem, you didn't follow all 7 steps. typically, failure to meticulously follow steps 1,2 and/or 3 is the problem.