LG Nexus 5 touch screen not responding
I had a similar problem. Dropped my Nexus 5 last night with screen facing downwards. There was no damage to the LCD and its power and volume buttons were working fine too. However phone stopped responding to any touch. I suspected its digitizer was broken. So I googled for a solution and whacked the screen a few times as suggested on few of the forums. Also came across a suggestion from someone who had a similar problem to keep it in a freezer for 30 seconds. Alas phone remained adamant and refused to embrace my touch.

I checked with LG service centre for the cost albeit it was a too expensive proposition to replace LCD and digitizer (apparently in Nexus 5 its one unit and in case of damage to either component, you need to go for both). 
With nothing to lose as a last ditch effort I kept my phone in the freezer again and forgot about it for an hour or so. Voila that did the trick and phone is alive again and working like a charm!