I'm running SH4 on Win 7 but I had to download the gold version from Ubisoft again. My disk version would not work.
I even downloaded (bought again) a version of SH3 from steam and it runs.
Have heart. Save your save games & campaigns found in your My Docs and restore them later.
At least they are cheap to buy again. It is frustrating I know. I had purchased extra copies of the disk games so I would have back ups!! Useless now.
Good luck.