Did you purchase Premiere Elements 8 as an online download from Adobe or did you purchase an installation disc in boxed packaging?
Adobe offers "Adobe Other Downloads" only as old as version 9. No 8. So does another web site.
Your major possibilities as I see it
a. If you purchased an online download from Adobe, then go to the Adobe web site http://www.adobe.com, sign in with your Adobe ID and password, type "My Orders" in the Search field there, and navigate to "My Orders" and your specific order for Premiere Elements 8. You may find another set of Premiere Elements 8 installation files for you to download.
b. Otherwise, you will need to purchase the program again to get new installation files or installation disc and new serial number. You will need to explore online to find out if any authorized reseller still has it in stock.
Right now Adobe's My Orders route seems to offer the most promise
Please update us on your progress.