How do I get information off my Nexus 4 if it won't turn on?

[justbree]

So my Nexus committed seppuku, and won't turn on or charge (yes I've tried every possible fix, including disconnecting the battery). The only sign of life is the red flashing LED when I hold the power button while it's charging.
I've already called Google and they're sending a replacement, but how do I get all the stuff off my current phone?

 

[anon(847090)]

not possible