Why doesn't it release the "click"?

I had a similar issue, and it turned out that the rubber feet had been warped and twisted. In my case, it happened because I was lifting a Mac Pro onto my desk and accidentally put some weight on the trackpad - the lateral movement shifted the feet slightly.

The rubber nubs on the bottom of the trackpad are small plastic pieces, covered with a small rubber flange. This rubber covering is thick over the exposed part of the feet and thin and quite wide underneath.

If you can get something thin and preferably flexible under the feet, move it around to smooth out the rubber. If that doesn't help, try popping the feet out with something small but not-as-flexible, then reseating the rubber covering and the feet, making sure there are no bunches.

I used the tweezers from a swiss army knife, and they worked fine. I wouldn't recommend something metal if you can avoid it though - it may rip through the rubber.

Good luck!