It has been awhile since I tried this so I'm probably not remembering correctly when I suggest this, but I'm going to try. You do have to use the compatibility mode of course. I had it running successfully on Vista, so I selected that option. Anyway, I think (remember I may not be remembering correctly) there is a system "check" it does during the load where it is checking your system's OS (you will see the message come up that it's checking your OS). As soon as you see this, uncheck the box so that it stops checking your system. Reason is because, this is a 10yr old program you're trying to load and it's looking for XP. So if you make it skip this step, it will continue to load successfully.
Like I said, I may not be remembering correctly, and if not then my apologies. But I think this is right.
Oracle has not, and is not, going to release a patch to make Oracle 9i run on Win 7. If my above info won't help you, you are going to have to upgrade to the current Oracle