Have to jump, runs rough, diesa few seconds after cables are removed?

2006 Ford Taurus 3.0L

Won't start without a jump, lots of clicking and lights blinking.
Jumped it and it took a bit to start, but eventually did. As soon as I pull off the jumper cables, it slowly idles down and chugs for a few seconds and dies.

I pulled a code P0353 (Ignition coil C primary/secondary circuit). I looked up possible causes by googling the code and it says:

- Faulty Ignition Coil 3
- Ignition Coil 3 harness is open or shorted
- Ignition Coil 3 circuit poor electrical connection
- Faulty Engine Control Module (ECM)

Any way to easily test this?

Take a friend with to a DIY car wash, INCASE! POWER WASH engine with GUNK ENGIne CLEANER ORANGE and remove All the corroosion and baked in JUNK under the hood! Take $20-30 to ANY OIL CHANGE PLACE and have your IDLE AIR CONTROL VALVE cleaned up to SHOWROOM CLEAN< as THIS is where the AIR/FUEL mixture is finally corrected at STARTING UP and during STOP and GO driving! A DIRTY IAC will make oil dirty quickly as well! REMOVE All COIL WIRING HARNESSES from coil and try to make them RESEAT themselves! CLEAN BATTERY TERMINALS and be SURE that the connectors are FULLY SEATED to the bottom of the BATTERY POSTS! USE ONLY MOBIL ONE 0W_30 or PENNZOIL ULTRA EURO oil in there for LONGEST LIFE and stay away from VALVOLINE OIL that NO factory uses ANYWHERE ON EARTH! It makes SLUDGE and leaves TAR and WAX coatings that can ruin a REAL European engine design like THIS ONE IS! Have BATTERY and CHARGE System tested at AUTOZONE for free, and get battery SLOW CHARGED there as well for FREE! THIS ENGINE is STARVING for AIR from as clogged up IAC valve and T body! Use AMSOIL POWER FOAM for this and run it THROUGH the PCV as well! Keep engine CLEAN with frequent washings with GUNK ORANGE! Use a can of CRC ELECTRICAL CLEANER SPRAY on COILS and WIRES to them! These are SUPERB< not just GOOD engines. That will last for 350k miles if you use the BEST OILS and change it ONCE a year only!

Often the coils start going, one at a time, usually its good to replace the wires at the same time, like spark plugs and wires. The procedure is not inexpensive, but not fixing will cause bigger problems. If the problem doesn't go away after changing the coil, look at the ECM.

Robert's info is not useful for this problem, but may be useful for general ongoing maintenance. Your problem may also include a corroded / weak battery, as indicated by the need to jump frequently, or a weak alternator to keep it charged while running. Alternately, you may have a device that is draining the battery while it is turned off. But start with the coil & wires, then charging system: battery, alternator.