The one that's currently in the Mac App store (iPhoto 11) requires that you be using Mavericks, OS X 10.9. Since you have Snow Leopard, you'll need to find an older version of iPhoto that will work. Off hand I don't remember which one will work with Snow Leopard.
iPhoto 09, v8.1.2 works fine with Snow Leopard. You can get it with iLife09 from Amazon:Off hand I don't remember which one will work with Snow Leopard.
Yes, it should have done. Perhaps it's secondhand and the previous owner deleted it.I'm confused. I didn't have to purchase iPhoto separately. It came pre-loaded when I bought the computer.