You will not find a serial number ON the box where anyone in the store may see the number
You will find a serial number or redemption INSIDE the box
What version of Premiere Elements and on what computer operating system is it running?
I purchase the boxed version of the Elements products from online vendors. These products have been coming with serial number that I can use in the disc installation process. With the above information, I can give you first hand account about where to find serial number if the product was sold with a serial number and not a redemption code or product code.
Did the seller tell you whether the product was being sold with a redemption code, product code, or serial number?