use your installation files to install on your new computer. you can migrate your catalogue: http://helpx.adobe.com/photoshop-elements/kb/backup-restore-move-catalog-photoshop.html
if you don't have your installation files 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.h tml
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.