Android - Control Android with broken screen from PC

adbcontrol can do this. It opens a window containing the phone screen on your computer, so you can use it when the phone screen is broken, and you can click and type in the window to control the phone. To install adbcontrol do:

wget http://marian.schedenig.name/wp-content/uploads/adbcontrol.zip
unzip adbcontrol.zip

Now edit config.properties and change:

adbCommand=/your/path/to/adb
localImageFilePath=/home/youruser/adbcontrol_screenshot.png

Save config.properties and run java -jar adbcontrol.jar which will open a window to remote control your phone. Make sure that adb works (adb shell opens a shell), and that the phone is awake so the screen is on (even if it's cracked/broken) otherwise you'll just get a black window.

One word: Vysor

Using the vysor to control my Xperia Z2. See the state of my phone, but Vysor came to the rescue.

*if phone reboots and won't connect after plugging in, try removing the micro sd card. Mine wouldn't work at all until I did so - random phone smasher

You could try to use AndroidScreenCast for you purposes - it's maintainable version of original androidscreencast. It requires only Java and ADB, no phone client, so just run it and use it. I've just tried it with Nexus 4, Android 4.1.2 Jelly Bean emulator. And, actually, I'm currently the maintainer of the project, so if you got any questions or issues - contact me via github.

And here's link for Windows bundle: androidscreencast.7z of latest release.