2004 ford taurus is running horrible

Repair Shop--- you installed too many parts already,
on a guess with no testing

Crank Position sensor then the timing belt are the next two steps in the sequence.

your problem may lie in a faulty fuel injector or an intake manifold leak.

by the throttle butterfly their is a steeper motor or a valve of some description but i think this vehicle has the standard one fitted and this has four wirs running to the plug ,two wires are earth and two are the feeds ,so to increase idle current is applied to one pair of wires and to lower ide current is applied to other two wires ,its a 12v feed which you should read as the idles goes up and the same on the other pair of wires when idle goes down the power runs a 12v DC motor which screws in or out ,you could run a bit of twin flex from battery and touch it to the connections to check its operation

3.0 OHV engine?

This is going to sound wierd but with the engine running and the noise preset stand in front of the vehicle and put your forehead on the intake manifold. If you hear the squeak in you right ear than it is the CMP shaft making the noise. Over time the bushings in the shaft wear out and the shaft will squeak and sound just like a belt squeak. eventually it will get bad enough that the engine will start to hesitate if not stall.

The easiest way to replace the shaft is by removing the upper plenum. The reposition the harness exposing the shaft/sensor. It is located on the drivers side of the engine right below the throttle body under the wiring harness that runs by the rear valve cover.

The shaft and sensor are available in the aftermarket.

The shaft is similar to a distributor shaft and will need to be in proper alignment. I can give you more detailed instruction if you decide to replace it yourself.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Any vacuum leaks? Timing good? egr and o2 sensors good?

If the car was running great and then all of a sudden it started this problem and you did not change the timing belt. Then I would say its not your timing belt. Once a timing belt is on its stays timed until it breaks, unless it looses a tooth on the belt and at that point it would run really ruff all the time or not at all. If it cranks well and idles with a small skip but when you add gas it get worse. I would look at your fuel injectors and spark plugs and wires. start simple and work towards the big stuff. most of the time its simple like plugs and wires or gummed up injectors. Run some good injector cleaner as well. Hope this helps

You are mis fireing on cyl 1 and 3 if you replaced plugs and wires and coil this is going to be a fuel injector issue or valve issue. See if you can swap the injectors with known good cyl. and see if it changes. Or have a shop do a fuel injector service on it to see if it helps. It may be to late for the fuel injector service.

check the vacuum hoses and make sure none of them are off and check the timing and also the drive belt

I had the same problem on my '02 Taurus, 3.0, V-6, 24 Valve engine. I replaced the plugs and plug wires which helped the problem but did not cure it. I then replaced the ignition coil (Motorcraft part # DG-485) which solved the problem. Has been running great since then...