Since your question is about Photoshop Elements, I have moved this from the Photoshop forum where you posted.
Also, to add to hatstead's answer, I am not sure if PSE7 was like PSE6, which had a serial code only linked with your physical DVD/CD copy and not to a download server. I don't see how you could get a downloadable installation file. I have kept copies of my PSE6 and PSE10 versions installers as well as the serial codes.
In the above link, scroll down to Individual>sign in to contact us. Try to establish a chat session with Adobe. I don't think that the download links for this old version of the software are available. It is also problematic that PSEv.7 will function flawlessly on a modern operating system.
It has been reported that a new version of PSE will become available later this Fall. If you can hold off until it is released, try out the 30-day trial to see if you like it.