Do you receive an error message when you try to install? It does look like Windows 2000 and XP were the current operating systems when Photoshop Elements 3 was released. It is certainly possible it may not be possible to install Photoshop Elements 3 under Windows 8.
You can also find details regarding Photoshop Elements 11 at http://www.adobe.com/products/photoshop-elements.html. Photoshop Elements 11 has been tested for Windows 8.