Q: Mazda 3 2010 has random starting issues

If the engine is not cranking, that is the starter motor is not engaging the flywheel and turning the engine over, that doesn’t implicate the ignition system (e.g., ignition coil(s)). A possible cause of your no start condition is the starter motor itself. The next time the starter fails to operate, try hitting the starter motor with a rubber mallet. If the car then starts when you turn the key, the problem is a weak spot on the armature in the starter motor; by tapping the motor you move the armature slightly. A more "sophisticated" approach to diagnosing this is, the next time you have a no start condition use a voltmeter to check for full battery voltage at the starter motor, while the key is held in the start position of course. If you see no, or low, voltage, during that test you have to trace the circuit to determine why no power is getting to the starter. However, if when the key is in the start position, power is being supplied to the starter, there is no voltage drop, and yet the starter doesn’t run, obviously that would mean you need a new starter motor. If you desire that a certified professional from YourMechanic diagnose the no start condition and, if need be replace the starter motor, please follow up to schedule a mobile diagnostic.