the thing that doesnt make sense to me is, you said it clicks but top doesnt go up or down.
now does it click while you are holding the button in, or does it only click when you push the button in and then release it?
if it is the former, i would check the relay. pull the carpet piece out of the trunk (one that is under where the top stowes). you will see two relays there. check them and all their connections. i would esp look at the power supply to the relay that feeds the motor. if it is getting miniscule juice from a bad fusable link or other malady, the relay will energize but not have enough amperage to move the motor. kind of like when your battery is almost dead and you try to start the car, and you get the "click, click, click." same thing, the relay (or starter solenoid) is energizing but there is not enough juice to awaken the top motor (or starter bendix).
good luck. let us know what you find and what happens. hard to find good info on soft tops.
BTW, while you are in there, might want to check your hydraulics fluid level. (not that it is a problem here, just cuz you are in there messing with the relays).
good luck.