What is wrong with a 1997 Saturn that will not turn over?

Probably dirty battery cables.

I have a 1994 SC2 that had the same problem, I checked the battery conditon, battery cable condition and had the starter tested and all were fine. It turns out that is was the ingnition wiring in the steering column. One of the wires was not making good connection, I found this out while trying to take the ingnition out to replace it. You will need a 5.5mm nut driver to take apart the steering column covers, and make sure you get the one behind the tilt lever.

It could be that but it can also be your starter. I also have a 93 Saturn sl2 that did the same thing to me. I replaced the starter with the the updated one that they have out and car started up afterwards. also.