If you already registered before on your old computer then you don't to do it again, however, if what your getting is the activation screen, then you do need to do that.
Recently i installed photoshop on a windows 7 system and besides being sure you have sp1 and all the recent updates, you'll most likely need the enable TLS 1.2 under How do I enable TLS 1.2 on Windows 7? on this page:
Thanks. Elements was registered with the previous install of windows 7. However, Elements is still demanding a re-registering on the new install. I have the latest browsers. However, Adobe say they no longer support Elements 7 on line. So, I am waiting for them to get back to me to resolve the problem. Fingers crossed that they don't just abandon anyone with an earlier version.