Non starting engine, rapid clicking noise

Mike, From your description of the problem, and given that the car was, prior to this attempted start, working properly, it soinds like you are not getting enough power to your starter solenoid to fully engage, thus the click. Start by checking your connections at the battery, make sure they are clean and tight, I would suggest you disconnect and clean thououghly with a wire terminal brush. Water and baking soda will help dissipate the acid build up. You may then spray the connections with a contact spray, (from your local auto parts store), then reconnect. Also if you think the battery is weak, you could try a boost when you attempt to re-crank. Your connection at the solenoid should also be checked and cleaned, although the problem is likely at the battery. Remember, it takes a lot more amps to engage the starter and spin your engine, than to turn on the lights and blow your horn. If this works, you should have your charging system checked for output..usually free at advance or autozone. The corrosion at the terminals works both ways, not only can it keep your car from cranking, it can impede charging of your battery as well. Hope this is helpful.

It's sounds like you have low voltage, this would allow for the lights to come on but no enough power to run the starter the battery might be bad or low from a bad alternator, either way you need to get the battery checked and your electrical charging system diagnosed for a specific repair. Most parts stores do this free of charge but you have to get the battery and the vehicle there first. I recommend you jump-start the vehicle and drive it straight to a store that performs this checks.