This does not necessarily mean your phone is dead. Your phone will flash the red LED light briefly when the battery is completely drained. When I got this I left the phone in the charger for a while, and eventually the white "charging battery" icon appeared again. Upon turning on the device it had 0% battery. It was in fact so drained that it died while on the charger (at 0%), so I left it to charge for longer. After it regained 30% of it's battery I took it to work and it seems to be draining, charging and working normally.
I'm not sure why lots of sites claim this means your phone is dead, lots of them just say "what else would a blinking red light mean", but definitely leave your phone plugged in for a while and attempt to turn it on again before you attempt to get your phone repaired.
Also if a normal microUSB doesn't seem to be working, try the original charger + wall wart that came with your Nexus 4. My dad had this issue with the N4 and other chargers didn't seem to work. Not sure if the volt/amp/something just isn't enough from other cables or what, but Google recommended it and it seemed to work.