Fuel pump/ relay/ wiring issues

Question edited for clarity.
Question moved to sub category.

P0304 is only a misfire error to cylinder 4.

https://www.700r4transmissionhq.com/p0304-kia-sedona/

There isn't a 'fuel control module'.

https://www.google.com/search?q=2005+Kia+Sedona+2EX+3.5+Fuel+control+module

But there is a fuel pressure regulator

https://www.google.com/search?q=2005+kia+sedona+fuel+pressure+regulator+location

When you look up fuel 'module', you come back to the fuel pump.

https://www.google.com/search?q=2005+kia+sedona+fuel+module+location

One thing you might try is moving coil pack 4 to another cylinder and see if the code moves. After that do a plug swap and see if it moves. Do them separately not coil and plug together..
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Your sure that B+ voltage is present at pin 30 ? If so an you measure no + battery voltage back at the fuel pump , you have an open circuit in that wire . Try supplying B + right to the fuel pump .

Kia Sedona Starting/Stalling/Idling Problems - Car Forums at ...

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Jul 10, 2006 - 31 posts - ‎16 authors
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Why does engine stall intermittently while ideling or driving ...

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I was leaving work, coasting to a stop sign, and it just quit. ... Why does engine stallintermittently while ideling or driving? on 2005 Kia Sedona ... But, the latest occurance left me and my family stranded 100 miles from home in freezing ... never wait to findout reasons for this kind of issue. they never get better by themselves ...

Idle Air Control Valve - Car Talk

community.cartalk.com/discussion/2285074/idle-air-co

Measure it.

Check coils (good spark on plugs), cam sensor and crank sensor. Check connections to the above and continuity of wiring.

I would check the fuel pressure and replace the fuel filter if it hasn't been replaced for awhile. The last 2 fuel filters I changed, the gas coming out of it looked like black ink.

Drop the fuel tank and replace the fuel pump. Filter is attached to the fuel pump. Sounds like the fuel pump is failing.

fuel pump is burned out from running out of gas, the pump is cooled by the gas it sits in inside the fuel tank, when you run low on fuel or out of gas you over heat the pump severely and the bearings in the pump seize up, have seen it dozens of times in my 30 years of dealer work.

Might have got some bad gas at one time and when gas is low in the tank whatever is in the tank clogges up the fuel pump screen.

http://www.kiatechinfo.com/index.asp

Good source for Kia its free to register NO STRINGS

check your tire pressure. also you may have injectors dumping to much fuel in the cylinders.