2005 Jeep Liberty Crank No Start

I have a 2005 Jeep Liberty with a crank no start condition except will start with accelerator on floor and will run while feathering throttle but runs rough and sounds like it may be missing.  If you allow vehicle to shut off as it will not idle it will not restart.  After allowing to shut off when attempting to restart will attempt to fire but will not start again without letting sit for a few hours. The spark system was checked by Pulling each coil individually and grounding out the spark plug and visualizing spark being produced by each individual coil and plug.  Fuel system was checked with a pressure gage and found to have 60psi.  TPS, IAC, ATS, MAP and all have reference 5.0volts.  Injectors are suspected of possibly sticking but will not drain pressure with KOEO.  ASD relay was checked and swapped with a known good relay even though original relay was good.  Concerned that PCM may be bad but will run as stated above.  Codes stored are P0038 and P0058 but o2 sensors were unplugged for testing and have not cleared.  Plan is to check injectors individually but without being able to have vehicle run will be time consuming. Any ideas or directions to go about diagnosing this vehicle will be appreciated.  Do not have a Oscilloscope but do have a test light and multimeter.  Thanks

What engine is in the Liberty?
Since you had the plugs out all ready, how did they look? Wet/dry, black, clean?
One thing that comes to mind is fuel contamination. If it is terribly old, has water, two stroke fuel from someones shed, diesel fuel etc...

Plugs were wet but not dirty. Smelled of fuel. Added fresh fuel to tank so should be good on fuel. Didnt have a HEI spark tester but plugged spark plug from each cylinder into the coils clamped with vice grips on hex flats and touched to engine ground and cranked engine. Visualized spark while testing each cylinder individually while cranking engine.

Today did sound check on each injector with long wood handle and long screwdriver with audible click heard. Then using test light with grounded clamp had assistant turn over engine and test light lit up when ignition on and while cranking. When no engine start after a few seconds light would go out. 3.7liter v6 chrysler/dodge/jeep engine.

For the sake of argument I would say that, hypothetically of course, if the tank somehow did have a few gallons of diesel fuel or something in it, adding fresh fuel to the tank would not correct this condition.
So contaminated fuel is still on the list of suspects as far as I am concerned until you take a fuel sample.
Based on your description of the checks you made at the injectors with the test light, (and since you have spark and 60psi fuel pressure ) it sounds like the ASD relay is working.
You said you suspect the injectors sticking, closed I assume? The wet plugs kind of makes think not, but if that was the cause of the no start it may fire on alternative fuel like brake cleaner, propane or starting fluid.

The fuel coming from the fuel rail is clear and smells of regular fuel no diesel oil contamination from my visual inspection and simple smell test. O2 sensors werent fully locked in by the clip so that corrected the P0058 code. Still have P0038 and that 02 sensor is stuck in pipe and difficult to get to so will address next when injectors are fully tested. On a whim pulled fuel rail and fuel injectors to do a spray patern test. Havent finished getting hooked up yet cause injectors were stuck in the ports of the head. Will report findings when finished.

Ok, fuel injectors are all working. Nice even spray. For now none are hanging open or leaking. Now spark system may be suspect. Voltage at all coil plugs are 0.14 on one wire and .03 other wire with KOEO. Although i was getting spark i may have a weak system and need to further investigate.

Sounds like the ASD relay had turned off by the time you made it to the coils with the multimeter. You know they have power because they make spark. I would move away from the ignition system. You're deep enough where it wouldn't be a too much work to perform a compression test on all cylinders with all the plugs out.
I would still take a good fuel sample in a glass jar to check for water and or alcohol, I would also try to burn a little bit outside (which doesn't always prove anything if it does burn), and spill a little somewhere it should dry up quickly. If it leaves an oily residue after the gas evaporates, no bueno.

Ill inspect the fuel a little closer to check for contamination and for being past its prime. I ordered a propper spark tester (lisle 20700). The way i tested the spark before was free from the combustion cycle and potentially could be too weak to light the fuel in the combustion cycle. I did another test with a test light and getting 12 volts on coil plug power wire with turning ignition switch that stops shortly after releasing key in a no run state. Also 12volts flickers on the signal wire when cranking also. Will report back after recieving the spark tester but wont be here till tomorrow.

did you do the compression test as mentioned early by fastestcackets and what was the results , sometimes rockers come off and by now you might have gas in your oil .

Plan for tonight is to check coils with lisle spark tester and do compression check. Ill post results and compression numbers when i get done for the night. Really cant see all the coils being that weak but we will see. Any scanner danner specific videos on testing the chrysler/dodge/jeep complete ignition system including ASD? Although ASD appears to work properly with voltages at relay and cutting power when no start occurs

I did another test with a test light and getting 12 volts on coil plug power wire with turning ignition switch that stops shortly after releasing key in a no run state.

This test (as well as others you mentioned) proves the ASD relay is working.
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Ok, got all coils checked with a a propper spark tester all checked out with nice strong spark. Moved onto compression check. Cylinders 1 and 2 no compression al all. Cylinders 3,4,5,6-170-180. Guess i am pulling valve covers to check rocker arms. Not familiar with this engine but learning quickly. Any experts who have dealt with slipped rockers and if replacement heads or engine the better repair in worse case senerio? Ill report findings. High milage engine not sure if overheated so could be dropped valve seat and rocker issue.

Compression test for the win!
Not great news, but now you know where you are going.
If you see anything cool, post pix please.
Surprised it never set misfire codes on one and two...

Never set a misfire code between the onboard heads up display or plug in code reader. Ill try to post pictures of what i find.

    Got the drivers side valve cover off and guess what we found? Two rocker arms laying in the head recesses.

I saw a vid by SOUTH MAIN AUTO awhile doing a job on a jeep . it might help you. look for that.