I have a Nexus 4, I've had it for 2-3 years running in Cyanogenmod rooted with no problems. It fell many times but nothing bad ever really happened to it until yesterday. It fell and had a tiny crack in the screen, then the screen was no longer responsive. I've seen many people with cracks in their screen able to use their phones but I guess that wasn't the case for the Nexus. Now since there's nothing wrong with the phone besides the screen, is there a way to control it from my PC? I find a screen replacement would cost as much I bought it.
I have found another app called Droid Explorer from CodePlex. Download the required setup(x86 or x64) and install it.
After installation, follow the video of Android Controlled from PC by MobileTechVideos. The video shows complete procedure of using Droid Explorer.
Hope this will help.
Requirement: Android SDK