The COPS (coils) may have shorted the drivers in the PCM (computer). You should get a misfire code for each cylinder misfiring though.
Slim possibility, but very expensive unless you have a service contract.
Some 1999-2004 Navigator, 2002-2003 Blackwood, 2003-2005 Aviator, 2003-2004 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.
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).
FOR VEHICLES WITH RUNS ROUGH/MISFIRE CONDITION:
- 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.
- 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.
- If cylinder leakage and compression tests are inconclusive, perform misfire diagnostic, per TSB 05-22-8.
DO NOT TRANSFER SPARK PLUGS. INSTALL NEW SPARK PLUGS IN REPLACEMENT CYLINDER HEAD AND CAM ASSEMBLY.
THE ENGINE MISFIRE CONCERN IS TYPICALLY EXHIBITED ON THE LEFT HAND CYLINDER HEAD AND RARELY ON THE RIGHT HAND CYLINDER HEAD. UNLESS CONFIRMED, THE RIGHT HAND CYLINDER HEAD SHOULD NOT BE REPLACED AS AN "EXTRA MEASURE" SERVICE PRECAUTION.
THE REPLACEMENT CYLINDER HEAD WILL NOT IMPROVE OR REDUCE ENGINE HORSEPOWER OR TORQUE ABOVE ADVERTISED LEVELS.