A clicking noise form the starter can be from not enough power from the battery.
The battery could be either a bit flat, or it may have a cell or two that are stuffed.
The headlight trick can possibly tell you if its a battery problem. If the headlights are dull, your problem is likely to be the battery.
If it is clicking when you are trying to start it, and the battery seems okay, it could be a bad earth connection.
You have some other problems, so that could well be the issue. Make sure you have a good heavy earth connection between the battery and the engine.
Clean up both ends and tighten them.
It could also be a faulty solenoid, or more likely, bad contacts in the solenoid. The bits that get the power through to the starter motor itself.
The solenoid can click in, and throw the bendix forward, but fail to make proper electrical contact for the motor to start spinning.
Using a convenient sized spanner across the two main terminals on the starter will show this problem.
WARNING!! WARNING!! DANGER WILL ROBINSON!!!
Make sure the car is in Park or neutral with the handbrake applied before trying this one.