I've had this problem before and it was usually related to getting juice to the starter. I've a '97 Grand Voyager, and often the problem was related to either a loose battery cable, corroded cables, or undercharged battery. If there was a lack of power, the lights may come on, but there isn't enough amperage able to crank the starter, resulting in the 'click click click'... I believe it was pushing the solenoid, but the motor can't crank the flywheel.
The solenoid is one of the most important parts of the starter... it makes the contact to run the starter motor. Another problem I've had is getting the starter to work but find out the solenoid (or motor) would get stuck. I once had someone hit the starter on the back with a hammer while trying to crank it, and it finally started. In this case I replaced the starter and haven't had a problem with the starter since.