Why don't you try different walking, like walking up and down hills, or swimming or something different? What about bike riding?
Pilates can be great to build lean muscle and help burn fat by building your muscles. Just be sure to tell the instuctor that you have a weaker floor so that they can modify certain moves for you.
I would definitely listen about the running and lifting weights though. I am never supposed to do them again now, and I need surgery.