Disconnect the battery and the connectors on the PCM/TCM and use a hairdryer to dry those connectors out as well as other electrical points in the engine bay.
Re-connect everything and see what happens.....also check all fuses under the hood and inside the cabin.
The PCM has very little to do with the starter being energized when the ignition key is turned....turning the key provides +12 volts to the top end of the Starter Relay (via fuse 8 under hood), the bottom end of the starter relay goes to ground by either the transmission being in Park or the transfer case being in Neutral.
If you remove the Starter Relay and jumper pins 30 and 87 in the relay socket the engine should turn over as you are now bypassing the ignition switch, the Starter relay and the transmission interlocks...the engine may or start or may not start...this is where the PCM comes into play...make sure you are in "park" when doing this.
If the engine does not turn over by jumping the relay as stated then either the fuse is blown or the ignition switch has the classic "Ignition Actuator Pin Broken" fault which may by coincidence have happened at the same time. This means removing the ignition switch off of the rear of the ignition cylinder actuator and try turning the ignition switch with a small flat screwdriver to see if the engine now turns over.
What year/model is your KJ?