You should be able to pull off the driver lower dash and access the plug for the ignition switch. If you measure the voltage with the key in the acc-off-on-start positions you should be able to build a chart that shows you have a constant power wires (12V in all positions), a constant ground, an accessory (12v in ACC and ON), a start (12V in START), and an Ignition 1 (12V in ON and START), there may be an Ignition 2 ( 12V in ACC, ON, and START).
You want to make sure your Start wire is working and Ignition 1, if either of these doesn't have 12V your vehicle will not start. If Ignition 1 doesn't have power the vehicle will not run or start, so most likely it is something with the start wire. If your ignition switch is bad the voltage on the wire won't be there.
The attached image shows the wires you should expect although it is from a 90 Cherokee so the colors may be different. The dark green is your start wire and yellow ignition 1 on the diagram. Hopefully your jeep's wires are the same color. Let me know how you make out.