Similar to this question except my LED light is solid blue.
I've googled the subject but the only thing that came up associated with the blue light was the Facebook app, which I don't even have installed. I can't say I remember ever seeing it before.
The battery was not low. The phone was unresponsive and, though off, the screen felt unusually hot. So I pulled the battery out and let it cool down. The battery's back in but it still won't power on.
I googled "nexus 4 hot", as my phone continues to be very warm (despite remaining, to all other appearances, utterly dead), and ended up on a Google support page, where I was able to chat with a live human being, who emailed me some troubleshooting steps, which were very basic and not at all helpful.
The email included a phone number, 1-855-83-NEXUS, where I talked to another human being, who again wasn't able to help, but was very pleasant.
No one has yet been able to explain the mysterious blue light.