Steph, `
If the car clicks and the lights work then the battery is fine. Also, that typcily means the alternator is fine since it properly charged the battery the last time the car was on. Not to mention, you can remove the alternator and the car will still start and run until the battery dies.
It might be the alarm. There are 2 ways to wire a starter interupt inside of an alarm or with an external relay. One is normaly open which means that if the alarm is not happy, then the starter wire is disconnected. This sucks if the alarm dies becuase that wire will never pass power until the alarm is fixed, replaced or removed. The other way is to have it wired normaly closed, which means so long as the alarm is not pissed, the car will start. So essentialy, the alarm must be going off to stop the car from starting so even if the alarm dies, the car still starts.
This brings us to what was clicking. If it was a realy under the dash, and the starter itself under the hood, then the alarm may be FUBR. If the clicking is from anything other then a relay for or within the alarm, then the alarm is not the issue. At that point it is either that the starter is dead, the spark plugs aren't firing, or you are not getting fuel to the engine.