The clicking you hear is most likely the starter solenoid. The way the circuitry works, when you trun the key to 'start', it energizes the starter solenoid coil. The solenoid has heavy duty contacts sufficient to carry the heavy current draw of the starter motor under load via their attachment to the battery. When you hear the clicking when you turn the key, you hear the solenoid pulling in it's contacts which supply current to power the starter motor. (the starter us usually grounded via its connection to the motor) If the starter motor does not respond and crank the engine via its gear mesh in the flywheel, then it seems therein lies your problem. Many things can be the problem: burned solenoid contacts; loose or coroded or dirty calbe from the battery to the solenoid contact. Weak starter motor etc.
Since modern starters are integrated with their solenoid It may be and often is that replacement of the starter/solenoid unit corrects the problem, since so doing usually exposes any cabling issues which may exist.
Now this is just my observation, to give you some perspective into your issue. It is also rudimentary, and not necessarily all that is involved in your issue with the crossfire. It may give you perspective when you discuss this issue with a professiional.

Rusty