About two years ago, I inherited about 100 old cameras plus a lot of accessories and gear along with them. I spent a couple of months going through everything, checking and evaluating it all. The steps I outlined come from my experience with all that stuff.
Most of what I said was just generic instructions based on my experience but I also have a Pentax ME Super, the newer "cousin" to your sister's camera. That's why I knew a few specifics.
My Pentax is a nice camera, I hope you and your sister can get your camera to work. You'll get a lot of nice pictures with it if you can.
P.S. - BMbikerider was right. The Pentax ME does not default to mechanical shutter if the battery dies. However, you can select the "100X" setting on the shutter dial and run the camera mechanically in an emergency.