Sorry to hear about this no start problem. What's more , you can't even look for trouble codes which adds to frustration. Hoping someone in our forum with some newer iron than me can help but it seems that the diagnostics will have to start from the battery . Thankfully , your battery is good or tracing voltage from where it exists to where it dosen't makes it more difficult to diagnose. An ohm meter is helpful but it is always better to physically find voltage to confirm where the problem. Start from the battery cables and make certain your getting power distribution and through the PDC . Make certain the starter , ignition and PCM fuses are good .
Eventually , you want to confirm if you are getting power to the ignition switch on the column . I'm assuming that absolutely nothing happens when you try to crank starter , so looking for voltage at solenoid wire to starter will not yield results. But with nothing happening when ignition is turned on , it must be confirmed if battery voltage is reaching ignition switch. You mentioned that the electrical system intermittently goes live with the key out ? To me , that means either the PCM got wet or water could have found its way down the side of the dash and got into the ignition switch and is causing intermittant connection or grounding. Just a guess since I actually have an issue like this with my '92 jeep XJ. While not experiencing any real blackouts like your jeep is , I do see irregular behavior from the wipers because the intermittant module which sits velcroed to the inside dash gets wet if water rolls down interior molding toward dash from top door post. Just a thought , but water does plague our jeeps and cause gremlins.
P.S. - sorry I forgot to mention , check PCM connections if loose and any signs of corrosion.
You may want to recheck your solenoid connections . Hope this helps.
