From whom did you purchase Premiere Elements (assumed version 13) and to what computer operating system.
At purchase I would expect that you were given a purchased serial number.
If you purchased from Adobe, consider going to the Adobe web site http://www.adobe.com, signing in with your Adobe ID and Password, tying in My Orders in the Search field, and following the My Orders link to your orders. Find your order. There you should have access to the installation files that you purchased. There should be 2, an exe and 7z file. There should be instructions to follow.
If you have any problems sorting out the details of your order, then the only one to deal with that is Adobe via its Adobe Chat orders.
To contact Adobe Chat Orders, click on the following link.
Membership, Account, Payment
Payments, Invoices, Orders
If the link does not hold its set, then you will need to navigate to the Chat Panel using the above titles as guides.
Please review and consider the above. Any questions or need clarification, please do not hesitate to ask.
Reminder, we are not Adobe here. Just user to user.