It's complicated since the SD card is coated/glued in. I used isopropanol to try and soften/remove the glue to no avail. Eventually I just used glue myself, glued a paper strip to the card and used that to carefull pull it out. There is some risk of damaging the slot in the process... Old thread:
https://www.mobileread.com/forums/sh...22#post4213922
Unless your card died completely or you somehow managed to brick the kernel (which the recovery/factory reset also uses) the built-in factory reset would be so much easier to use. However if you don't even get the Power LED to light up then you might not have much other choice. Things are really wrong when the LED stops working altogether.
It's possible your battery ran flat if it somehow got stuck on the firmware upgrade process. Charge it for a few hours if you haven't tried it already.