The only other thing that I can think of why the keyboard clicks stopped is that perhaps system sounds got muted somehow. I post this explanation from time to time here and it has helped some others.
System sounds can be muted and controlled two different ways. The screen lock rotation can be controlled in the same manner as well.
Settings>General>Use Side Switch to: Mute System sounds. If this option is selected, the switch on the side of the iPad above the volume rocker will mute system sounds.
If you choose Lock Screen Rotation, then the switch locks the screen. If the screen is locked, you will see a lock icon in the upper right corner next to the battery indicator gauge.
If you have the side switch set to lock screen rotation then the system sound control is in the task bar. Double tap the home button and in the task bar at the bottom, swipe all the way to the right. The speaker icon is all the way to the left. Tap on it and system sounds will return.
If you have the side switch set to mute system sounds, then the screen lock rotation can be accessed via the task bar in the same manner as described above.
This support article from Apple explains how the side switch works.
http://support.apple.com/kb/HT4085
But let me say again, that if you are having issues that are sound related and you have checked all of your settings, you probably should take your iPad to an Apple Store, there could be something very simple that we are missing and if its something hardware related, your iPad is still under warranty.