Have you put a DMM on the battery terminals to verify that you have enough voltage? Also find a nice paint free section inside your engine compartment and put the negative probe of the DMM on that with the positive probe on the positive side of the battery. This will verify that you have a good ground in the system.
Any other issues that happened right before this symptom? Anything else go wrong recently? This sounds like an electrical issue. If it were mechanical usually you would hear the system try to crank over. The only mechanical (also technically electrical) issue that I can think that would cause this is a bad starter or bad section on your starter.
The clicking could be the starter trying to crank. I haven't tried this on your car but you might be able to rotate the starter motor to another spot on its rotation. Sometimes the contacts within the Starter go bad and you can get it to start by rotating it a 1/4 turn or so. Good luck.