In a 96 Jeep not many sensors are involved. Basically Fuel and spark delivery at right time should start car if your Starter is able to crank the Engine.
If engine is cranking then the battery is Okay. Check Spark directly at the spark plugs and fuel pressure at the fuel rail. You may pull out one spark plug and check spark out of engine.
Try spraying Starting fluid in Air Intake while cranking. If Jeep starts then not enough fuel is being delivered by fuel pump. If you find no spark at plugs then check circuit for starter relay, Crank sensor/cam sensor problems.
A kill switch or bad Alarm system can also cause this problem.
Here is the Elec Diagram:
http://www.alldatapro.com/alldata/PRO~V451756054~C28087~R0~OB0~P4R0H~N/0/41746574/56418469/56418476/56418477/34853741/34864081/56251052/56251070/55276088/76721401/58958330/57479434
I’m happy to assist further over the phone at
https://www.6ya.com/expert/uttamjeet_2f3adc18600f8ede
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