Two suggestion for apps, mine, but there are undoubtedly others like them.
adbgrab.exe is a Windows application that will mirror your device's screen and allow you to mouse click. It works over ADB and is very slow, but will get you somewhere with a broken screen or touch sensor.
http://www.temblast.com/adbgrab.htm
UsbMode.apk is an Android application that does a few things, one of which is to show touches. All of the screen (besides the GUI buttons) will react.
http://www.temblast.com/android.htm
You can also go into Developer Options and enable "Show touches".