1996 Dodge Intrepid 3.5L: P0303, OBD-II Codes 12 & 43 - Misfire at Idle and Cold Start Diagnosis

Hi everyone, I own a 1996 Dodge Intrepid with a 3.5L engine, currently at 185,000 miles. I haven't had a tune-up in over 4 years (last one at 70,000 miles), and the vehicle has never overheated—always showing good power and smooth acceleration. Recently, however, it's started misfiring, initially only at idle. Now, since temperatures have dropped below freezing, the engine consistently misfires from startup until it warms up. Once warmed, the misfire occurs intermittently—about every 30 seconds—as a brief 'hiccup' in performance. I performed an OBD-II diagnostic using the standard ignition cycle (key on-off-on-off-on), and the check engine light flashed two codes: - Code 12: "Problem with battery connection; direct battery input to controller disconnected within the last 50 ignition key-on signals." - Code 43: "Peak primary circuit current not achieved with maximum dwell time." I then used an OBD-II scan tool, which revealed a single code: P0303 — 'Cylinder #3 misfire'. Given this, I'm suspecting either faulty spark plug wires or a worn-out coil pack in cylinder 3. Any insights into what could be causing these symptoms and codes? How should I prioritize troubleshooting steps? Thanks for any advice!