I have downloaded and run S12.1 on Win 7RC with no problems - and so have many others.
Obviously something went wrong during the Win7 upgrade (registry perhaps) but there are 3 things you can do.
I am not familiar with S12 but I believe you can repair S12 from the installation disc. However if Win7 cannot find Studio there is a chance that the installation disc won't either.
Second, uninstall S12, use the Pinnacle registry cleaner, and reinstall Studio.
If all else fails, back up all your data and do a clean install of Win7. You will need your Vista disc on hand when doing this. Replace your data and reinstall all your programs. I know this sounds drastic but it is sometimes preferable to start with a clean new system. With the new features on Win7 you may want to rearrange the way you do things anyway.