I haven't tried this test myself on a 91, sooooo?
http://www.naxja.org/forum/showthread.php?t=1062027
If you turn the key to the run position and get no CEL (check engine light) it is a good possibility the 91 is the same as many later years and you have a short in the 5 volt (in some early models it is 7 volts on some 8 volts) sensor supply circuit. If you get no CEL a simple test is to unplug the CPS and see if the light comes on, then unplug the Cam Sync Sensor, etc.
I usually volt test the orange wire (on many XJ's) going into the distributor and see what I get, if it reads 2-3 volts or so you likely have a short someplace in a sensor.
New parts don't necessarily mean good parts, changing out parts is a step in the troubleshooting process, but you never really know if the connectors are good (clean and making good contact) or there is something in the wiring.
It is always a good idea to grab a flashlight and check the normal culprits before you do much of anything else, The wire going to the rear O2 sensor, the wiring for the front O2 sensor (by the manifold down pipe and in the front where the harness goes up to the injector harness). The wires running from the CPS to the connector near the injector harness.
Coil to distributor cap high voltage wire and the wires running into the distributor for the cam sync sensor.
Coils are know to fail, especially the ones mounted to the side of the motor (heat). Check for in voltage to the coil with the key in the run position, Check coil continuity.
The most common failure is the CPS (like I said new doesn't mean good) secondly burnt wiring on the manifold or exhaust.
Looking at the CPS to see if it is covered in oil, mud or other crap is also a good idea. No CPS pilse during cranking, weak CPS pulse during cranking, interrupted CPS pulse during cranking ( dirty, corroded, full of water or oil connector or damaged wiring) and the PCM will shut down fuel (except for the initial priming) and shut down spark.
.