The "click" may be the starter solenoid. There are other relays which can "click". Open the hood, as someone turns the ignition key to START (III), listen for the click at the starter. Hear it?
If it is the starter solenoid clicking, and the engine isn't turning over, there are two major possibilities: the engine is jammed and CAN'T turned over (Something broke inside the engine. Have you ever changed the timing belt?); or there isn't enough voltage, and current, reaching the the starter to energize it.
Poor electrical connections can drop the voltage, and current, too low to crank the engine.