Why will a 1997 Jeep Wrangler turn over but not start with a new battery if it worked before the battery went dead?

Did you hook the battery up backwards before realizing the wrong polarity? Kiss the PCM goodbye.

Did you take the nice thin plastic cap off the negative pole that is placed on some batteries?. It's easy to miss if you are not looking for it and paying close attention. It's also possible that the new batter was DOA (Dead on Arrival), it can happen.