Chosen Solution

Phone was dropped and got a small crack on screen. No longer responds to touch. How can I tell if I need to replace the digitizer or the underlying LCD screen?

Looks like it is one piece: Nexus 4 (GSM) Screen Here’s how to fix it: Nexus 4 Display Assembly Replacement

I recommend taking it to a phone repair store, like at a mall, show it to them, they will tell you what is wrong with it, and will tell how much it would cost to get it fix.