One of the first questions to address is whether there's enough refrigerant in the system. It will not engage when the system is low. There is a switch located on the receiver/drier which will shut the system off if the pressure goes either too high or too low. You might first try bypassing that switch, just for a moment, and see if the compressor engages. If it does, stop immediately, and don't run it again until you have refilled the system. You can damage the compressor if you run it long like that. If the compressor still doesn't run, you should check the relays - there's one for the compressor clutch, but its location will vary with the year of your XJ. YOu might try just bypassing the relays and connecting the compressor clutch directly to 12 volts, to see if it works. If it does not, then the clutch may be bad. If it works, you'll have to trace the problem back through the system, starting with the relays.
The usual cause, though, is simply low refrigerant pressure.
By the way, I just noticed your location, and just have to ask....why are you worrying about air conditioning in March in Alaska? Here in Vermont there are about 3 days in a year when I think to myself "I wish I hadn't ripped the air conditioner out of my Jeep," and they don't come around until July.
