Engine missing and shows codes P0304 and P0316

The P0316 DTC code is a generic code that applies to all vehicles. This code means the powertrain control module (PCM) has detected a misfire shortly after startup, specifically within the first 1,000 revolutions. This code may also be triggered with another of the other misfire codes which are P0300, P0301, P0302, P0303, P0304, P0305, P0306, P0307, P0308, P0309, P0310, P0311, P0312. If you have another misfire trouble code also, you should diagnose and repair that code(s) first. Symptoms Symptoms of a P0316 DTC may include: MIL (Malfunction indicator lamp) illumination Rough engine start or idle Potential Causes Potential causes of this misfire code may include: Damaged or defective Crankshaft Position Sensor (CKP) CKP sensor wiring or connector fault Poor fuel quality Ran out of fuel Ignition system malfunction Fuel system malfunction: injector or fuel pump Mechanical engine problem Damaged PCM Possible Solutions First off, you'll want to repair any other misfire DTC codes if present prior to diagnosing this code. If you own a Ford vehicle and you have a P0316 along with one of the other misfire codes, you should check for appropriate TSBs (technical service bulletins), as there are some TSBs that in part involve reprogramming the PCM. Doing that requires specialized equipment. Some Ford vehicles even needed a new cylinder head as a result of the valve. Regardless, if you have a Ford with multiple misfire codes including this one, check for TSBs. If the P0316 is the only code, then it's time to do a bit more diagnosing of the crankshaft and camshaft position sensors, and their associated connectors and wiring. A tip we've found is "Since this code indicates a start up misfire, pay attention to items which may expand or contract when cold (if the code sets when the engine is cold), or hot (if the code sets on a hot restart)." Realistically, the freeze frame data from the PCM will be helpful in tracking down the problem. As will a good DVOM (digital volt-ohm meter), so you can perform tests on the wiring and the sensors.

Read more at: http://www.obd-codes.com/p0316
Copyright OBD-Codes.com

Code 316 means the engine computer has detected a miss-fire on startup. You normally get a code for the cylinder causing the problem.
If the spark plugs are original, I would start with checking them for signs of damage or excessive wear.

Here's the info. on P0316 here's code P0304,here's code P0305,here's P0171.

You have a misfire on #3 for code p0303 & misfire for code p0316

2004 Marauder and 2003-2004 Mustang vehicles built before 12/19/2004 equipped with 4.6L 4V/5.4 4V engine may exhibit a runs rough, lacks power, and engine misfire, prompted by a MIL light and DTC codes P0301, P0302, P0303, P0304, P0305, P0306, P0307, P0308, and P0316.
ACTION
Diagnose engine for engine misfire concern. If diagnostics determine an engine misfire which is characterized by leakage through exhaust valve(s), only replace the affected cylinder head(s).
SERVICE PROCEDURE FOR VEHICLES WITH RUNS ROUGH/MISFIRE CONDITION:
1. Perform relative compression check on all cylinders. If abnormal, check cylinder leakage and actual compression for "low" cylinders refer to Workshop Manual (WSM), Section 303-00.
2. If leakage/compression check indicates a valve train concern, per valve train diagnostics in WSM, Section 303-00, replace cylinder head and cam assembly, pipe plugs and timing chain tensioner, per procedure outlined in WSM, Section 303-01.
3. If cylinder leakage and compression tests are inconclusive, perform misfire diagnostic, per TSB 05-22-8.

So

P0316 = engine misfire
P0304 = #4 cyl
A very common problem is a bad COP or coil. They can be expensive ($75? at part store), so you could try switching the coil with another cylinder and see if the code changes location with the coil.
They are easy to replace. Unplug the connector. Remove the one screw (8mm?). Pull straight out.

pic up a manual at the zone-it has the standard list what each code signifies-remember they dont always tell u the solution cause physical problems in engine require inspection

P0304 cylinder misfire # 4, P0305 cylinder misfire #5 & P0316 cylinder misfire detected on startup. Start with easy first. Spark plugs &/or wires.

hi your codes show downstream o2 sensor oxygen sensor evapsystem o2 heater random misfire u need to check these

P0304 is Cylinder 4-misfire detected-probable cause is as follows. Engine mechanical fault, wiring, ignition/fuel system, injector, ECT/MAF sensor, ECM

P0316 Misfire detected during startup-first 1000 revolutions- probable cause is as follows-Engine mechanical fault, wiring, ignition/fuel system, injector