I have a 2004 F-150 with a 5.4L triton new style 3V. Two .months ago. It just gave out. I was having problems with idling. At red lights I would have to hold the brake and keep the RPM's at 1000 or higher. Or it would sputter or shut off. Then one morning I started it up and it was shaking badly. I hit the gas and it wouldnt move. It has no power. It slightly bogs down when I hit the gas. It has low RPM's. I changed the oil filter. Oil. Fuel filter. I ran a test on it. It said it has a miss in cylinders 6-8. I changed spark plugs. Coil packs. Wires. Checked vacuum hoses. Timing. Gaskets. Fuel pump. Replaced the computer and had it reprogrammed. I was told to check the catalytic converter on the drivers side but haven't gotten to that. Being as its my only vehicle and fiance is about due with our child I'm in a hurry to find the problem. But I do not know what else to try but can't afford to take it to a shop. Ford wants $85 an hr just to diagnose it.

 

I would think the cat is clogged

 

Would that cause only 3 cylinders on that side to go out and not all four though. That's what I'm checking next anyway.

 

One way to check for exhaust restriction is to drill small (1/8") holes before the suspected location and after it and use a gauge to tell the pressures. You may not need any gauges or fittings if the front hole blows hard, then put the screw in it and check the back hole, which would be hardly blowing. You seal the holes with self-tapping screws. Another way is to take the exhaust system apart before the cat and see if the engine runs better. I would recommend you go to a muffler shop and get them to check it. Assuming single exhaust, you should be able to tell by having somebody rev it up and observe exhaust flow, which should be minimal. You might also hear a 'hissing' from the exhaust because of the restriction.
Then there's the 'gorilla' method - you take a piece of wood like a bat and beat on the suspected cat. The object is to break loose some clogging material on the inside. Sometimes it will run better after that, and you know where the problem is.
But, there's no doubt you will have to spend some money on it. I think you will minimize your cash outlay by going to the local muffler shop. They deal with cat. converters every day and can probably diagnose it right away. Then you can decide how to go about the replacement - DIY or have them or Ford do it.
Cats are notorious on trucks because they use so much more fuel than small cars. And, if the engine uses some oil, you are almost guaranteed to get a clogged cat.