What does a solid blue LED light mean on my Nexus 4 phone?
This post MAY assist you (similar symptoms  but no Blue light... worth a try):

http://forums.androidcentral.com/google-nexus-4/312151-solved-nexus-4-wont-turn-charge.html

Basically it states to try to get your phone into "recovery mode" and then select "Start"... See if this at least wakes up your phone.

It includes a link to this YouTube video with step-by-step instructions:

https://www.youtube.com/watch?feature=player_embedded&amp;v=e0FVHFg6t2I#t=159