Battery is most likely, as the starter will click as it tries to engage, but does not have enough power to run the starter motor. If the battery is more than three years old, is low on water (if it is the type that has removable caps), or appears to
be bulging at the sides, it should be replaced.
Check the battery connections. If the car will start normally with a jump start, then the starter is probably OK.
Unless the alternator light was on, I would not suspect the alternator. Measure the voltage at the battery with the engine running, and you should get well over 14 volts with a normal alternator.
Walter
February 2008