I suggest the elliptical and stationary bike. The pounding isn't going to be good for the knees! You'll end up needing knee replacement.
Sorry to hear about your shin splits Mrs Hall. I'm in same boat, it hurts to run anymore. You could try either of these two things. 1) Indoor track with padded surface, or 2) walk for half an hour or so. Another option, one that I do myself is hop on an elliptical machine, they are easy on the joints.
Have you tried proper running footwear? You need something that is going to protect you whilst you run.