Engine won't turn over

I have a 96 Mercury Sable that has recently had trouble starting. The engine turns over slowly or not at all. Originally, I thought that the starter was going out, but the car has started fine with jumper cables the few times that it has died. However, when I changed batteries this evening (with a known good battery) I have encountered the same problem and this time the car won't start at all. I still have electrical power to the car (dash lights, radio, etc) but the car simply won't start or turn over. I am at a loss at this point since the car has always started with jumper cables. Would a starter cause this type of problem?

 

Check your ground and cable connections closely for tightness and lack of corrosion.