Many Sony reader models have not done well recharging through the PC USB port. What has helped is OVERNIGHT charging with a wall mounted AC/DC unit.
Suggest that you charge the unit overnight and retry the SD card rescue operation.
https://wiki.mobileread.com/wiki/PRST...bricked_device
Perhaps your battery is very low and not responding at this point even though it was hooked up to a PC....
Good luck!