Error Code P0304 & Trouble-Shooting?

Ahoy !
S-Type 2002 4.0L V8 Naturally Aspirated; VIN:…M24354; LH drive; 68k miles (previous owner let it sit in the driveway mostly.)
Finally got a chance to translate the Engine Malfunction Light into an error code and this at the courtesy of the State Emissions Inspection facility.
Got a P0304 error code that Mechanic Google tells me is No. 4 cylinder mis-fire error code
Am I on the right track ?
From searches on Google, No. 4 cylinder is closest to firewall, passenger side (RH)
Trouble-shooting easiest/most likely to difficult/least likely -
For No. 4 cylinder -

  1. Loose/Broken connector at the coil
    Action: Inspect connexion; if loose or bad connector then fix and see if error code changes. No change then,
  2. Faulty coil
  3. Faulty spark plug
    Action: Swap coils with another cylinder and see if error code changes. If No change then, swap spark plugs. If no change then
  4. Loose/broken connector at the injector.
    Action: Inspect connexion; if loose or bad connector then fix and see if error code changes. No change then,
  5. Faulty injector
    Action: Can I use a stethoscope to hear if injector is firing ? Or, Swap injectors with another cylinder and see if error code changes. If No change then,
  6. Intake manifold leak at No.4
  7. Low compression in No. 4
    Action: Go inside, mix a beverage and drub fingers on the table top.

Thank you.
Nuts: Lost the tolerable weather.

Regards,
Richard Cielec
Greater Chicago Metro, U.S.A.

In the five years I have owned my S Type, same year and model as yours, I have had to change five coils. On each occasion the misfire was intermittent, not solid. The original coils do seem to be a weak point. I have used NGK replacements and they have been good so far.

If I wasn’t so cheap I would have changed all eight in one go and saved myself a lot of trouble because some of the bolts that secure the coil covers are very awkward to reach. Access is improved if you can remove the cross brace but my bolts are all seized.

None of the misfires were solid enough to raise a fault code but even without, you can find the misfiring cylinder if your scanner has mode 6.

Hello, Mr. Capron:
Thanks for the tip the coils may be the likely suspect and additional thanks for the tip that I should seriously consider changing all the coils and to NGK.
Re: “cheap”. Reminds me of a line from the film “One Hundred Foot Journey”: 'Tis something like: “Asking for a discount doesn’t mean I am poor, it means I am frugal.”. Yes, indeed: Well reasoned, risk and effort assessed frugality in car repairs. May not be the quickest path to getting back on the road but, by gosh, the satisfaction of identifying the exact cause of the problem is glorious. I state this honestly, not a spritz of irony.
Re: Seized cross-brace bolts. I took the “Damn the torpedoes !” approach. Allowed each of the seven bolts (someone’s subtle joke on the dwarves, perhaps ?) to loose their respective head during extraction then, drilled-out and inserted heli-coils. Great fun ! Fa la.
Re: Fault code: Code 0304 indicates No. 4 cylinder (as per my Google search). (Ah…"mode 6:. Thanks. Another something for me to consider in my possible and likely hunt for an OBD device.)
Regards,
Richard Cielec
Greater Chicago Metro, U.S.A.