That doesn't sound good. In particular, the fact that it crashed (or re-crashed) during an update is potentially very, very bad.
(FWIW, the screen doesn't actually refresh until somewhat late in the initial boot process, which in itself is another good indicator that something seriously bad happened if you see the LED & backlight react, but not the later stages).
And since this is a PW, short of opening it up and babysitting the boot process over serial, your best bet might very well be a call to Kindle CS.
On a more general note: letting the battery of a Kindle go flat, even to try to debug an issue, is nearly always a very, very bad idea, no matter the model
.