When I go to inspection all my O2 and catalyst monitors will not complete a drive cycle?

Hello, what codes are the PCM setting? If it doesn't pass the IM Readiness monitors for the Oxygen sensors after 2 drive cycles, it will set codes. So, there must be something stored in the PCM. If the oxygen sensor switching time or the sensors are hanging high or low voltage, it won't pass any monitors, Ill post the list of codes, but also checking the exhaust back pressure to determine any Catalytic Converter failures would be good to know as well.
But any codes we'll need to know first. That will give some direction for diagnosing the issue.
If you have a scan tool, and can check the live engine data, you can take a look at the Oxygen sensors voltage levels and see if anything looks off. If any of the oxygen sensor heater circuits are not working, it will prevent the sensors from functioning correctly. I'm not sure what kind of shop you've had it at, but they should have given you a more in-depth answer about what exactly is wrong with the PCM. Such as if the memory circuit is losing or has no power. There is a battery feed that keeps power to the PCM to retain memory, which might be something they were meaning, but they should be more specific with the issue so you can get things fixed up right, instead of just replacing a computer.
But here's the service info on the IM Readiness monitors you need. So, if the PCM is not storing any codes, which almost sounds like what is happening, you can check that the PCM's memory circuit is okay.

Here are the fuses that are permanent battery feeds that retain the memory, Fuse 29 15amp, Fuse 20 15amp, and Fuse 5 7.5amp. They are kind of difficult to see on the wiring diagram. The 6th diagram shows the PCM Grounds, if there are any broken grounding straps or corroded grounds to the frame or body, or any voltage drop from the engine block to battery negative, or the frame to the battery, this can have the same effect as a bad PCM ground. So, check those fuses for power on both sides, here are some guides to help.
We should be able to help you figure out why you're not getting the monitors passed.

https://www.2carpros.com/articles/how-to-check-a-car-fuse

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

https://www.2carpros.com/articles/how-to-use-a-voltmeter

Have any codes been stored in the PCM? There must be some, if not let me know, and do other Readiness monitors pass? As for the Oxygen sensor voltage, the Bank 1 Sensor 1 and Bank 2 Sensor 1 voltages should be swing from about 0.2 volts to 0.8volts, in that range, the Bank 1 and Bank 2 Sensor 2 oxygen sensors (these are the sensors after the Cat) should be semi steady in voltage and not be swinging in that voltage range.
Below is an example of the Oxygen sensor voltage switching, you can see the first half of the waveform is normal switching, whereas the 2nd half is a slower (lazy) oxygen sensor, it is also hanging low voltage, this is a lean exhaust type of sensor signal.
But if there are no codes setting at all in the PCM, we need to figure why, it will be checking for voltage on the "Hot at all times" fuses, If no codes are setting, that needs to be repaired first or it won't matter what the oxygen sensor voltage is, because the PCM is not storing any data.

Hey Jeff, okay, what transmission code was it? The PCM controls the transmission.

Okay, so, you're switching on the rear oxygen sensors, are they mirroring the front sensors in their voltage switching? If they are swinging up and down like the front 02 sensors, then it sounds like the catalytic converters are not storing oxygen and may be failing. Fords take forever to set codes, much longer than any other manufacturer. I own one too, to further check the catalytic converters, you can do a back pressure test at the front oxygen sensor locations, by removing the sensors and starting the truck for a minute to get a pressure reading, although your converters might not be at the melt down stage yet. Another test is checking the temperature at the inlet and outlet of the converters with a temperature probe. This guide will show some examples of testing. I would be interested in seeing the rear oxygen sensor voltage reading graphed such as the diagrams I posted above, those are from a scan tools live data reading the PCM. I'm not sure if you have a scan tool that can read live data or not, but comparing the front B1S1 to B1S2 voltages you can determine if the converters are not doing their job and that's why the Monitors are not passing. Same with B2S1 and B2S2 voltage. The rears ones should not fluctuate like the fronts, they should be a steady voltage, usually around 0.7v (700mv) area. Ford will charge you a lot of money to diagnose and change the converters, so it's best if you can do the diagnosis yourself.
If you want, I can explain the back pressure testing in more detail, as well as scan data if you own a scan tool
Also, have you taken a look at your spark plugs lately? Do they have carbon or soot build up on them?

https://www.2carpros.com/articles/how-to-test-a-catalytic-converter

Yes, that is why the I/M Readiness monitors are not passing, The PCM monitors the converters by the Oxygen sensor signals, so bad broken up substrate of the converters will cause the Oxygen sensors and the Catalyst to fail those monitors, I'm sure with a restricted exhaust you had a lack of power that will return when the new converters are put on. Just FYI, the converters fail because of cylinder misfires or rich exhaust. So, if the PCM's Long Term and Short-Term Fuel Trims are higher than 10% either positive or negative, that is an issue that needs to be figured out. The fuel trims are something you will be able to read on a scan tool in the live engine data. They might be labelled LTFT and STFT in the data list.

A couple last things. Since the converters substrate has broken up into pieces, when replacing the them, take down the muffler and check the rest of the exhaust to verify that no pieces of the converters have gotten stuck in the baffles of the muffler, many shops never check this, but when the converter got hot enough to melt down, that break up into pieces, there is almost always sections that travel down the exhaust and get caught up in the muffler's baffles, this too causes a restriction in the exhaust, just at a different section. I have seen brand new converters put on vehicles, but because the muffler or rest of the exhaust wasn't checked, it causes excessive back pressure and can cause the new converters to overheat, damaging additional components, this being a Ford, check that the DPFE sensor has not over heated as well. The DPFE (Delta Pressure Feedback sensor) is a pressure sensor for the EGR valve, it's the sensor that has 2 tubes running down to the exhaust pipe or exhaust manifold. The sensor is usually mounted on the driver's side of the engine or on the back near the firewall, but when a converter melts down and blocks off the exhaust, these sensors being mounted to the exhaust will melt down or overheat the circuit board inside. Being that they read exhaust pressure differential when the EGR valve opens. The sensor is pretty easy to find, there are 2 steel tubes attached to the rubber tubes in the diagram below.

The bottom 2 in the 11st picture SHRTFT1% and LONGFT1%. The 1 stands for Bank1 of the engine, so there should be a SHFTFT2% etc, as well, was the repair done already?

Well, if both side Catalytic converters are broken apart inside, then they are done. I'm not sure what the inspection laws are in your state, every state is different. But you'll have to replace the Cats to get the IM Readiness to pass, as well as to pass emissions. They are both the same really, if the Check Engine light is on, it will fail. You don't need to replace the muffler and rest of the exhaust; I was just starting to inspect the rest for any pieces of the converters that have travelled down the exhaust. You can usually get them out of the muffler(s),
Take a look on Rockauto com. They have decent prices, but things get more expensive if you have a California or Federal emissions vehicle, the tag under the hood should say which one it is. California has much stricter laws when it comes to emissions. I'm not sure how accurate the scan data is on that Foxwell scan tool. I see that it's in Closed loop so it must be up to operating temperature. But I would expect the Fuel trim numbers to be more negative than they are. Did you inspect the converters yourself and see the actually broken apart? And is this the F-150 5.4L heritage edition? With or without a Turbo? If you're unsure I can look up your particular vehicle better by the VIN. I'm seeing some different service info depending on model.

Yeah, the OEM will always be super high for stock components. rockauto has some for around 250 and higher. What was wrong with the exhaust manifold? Was it cracked or broken? I just want to figure out why that side converter went bad.

https://www.rockauto.com/en/catalog/ford,2004,f-150,5.4l+v8,1422751,exhaust+&+emission,catalytic+converter,5808

If the exhaust manifold was leaking then the oxygen sensor on that bank was reading lean when it shouldn't have been, and that's what probably caused the converter to fail, too much fuel down that bank of the exhaust, overheated the converter and sent it into meltdown, then they break apart into pieces. So, that's what I think caused that failure. Usually, it's a misfiring cylinder causing the same thing, too much fuel going down to the converter overheating it, and bam. Meltdown. A leaking exhaust manifold is a logical reason for that converter's premature failure.