Updated July 24th, 2016.
If your laptop’s trackpad won’t click anymore, but otherwise it works fine, the problem might not be the trackpad! Weird but true. The problem might be your laptop’s battery, because when the battery goes bad, it swells, and when it swells, it presses up against the trackpad. Which makes it difficult– maybe impossible– for the trackpad to click. I saw this exact problem last week.
The good news is that Mac laptop batteries are roughly $100, a lot less than a new trackpad. And, assuming your laptop has the kind of battery that comes out easily, you can replace it yourself in minutes.
So… if your laptop’s trackpad isn’t clicking right, turn the machine over, take the battery out, and see if it looks all bulgy. Turn the laptop over and see if the trackpad clicks with the battery out. If it does, and if that battery is bulgy, buy a new battery and the problem is solved.
BONUS TIP: the trackpad surface is made of glass. Don’t try to fix a trackpad by pressing extra hard on it because you can break it if you press hard enough. And you’ll have to send the Mac in for repairs because you can’t replace the trackpad yourself.