How can I determine which block device corresponds to internal memory?
As Izzy said INTERNAL STORAGE usually refers to /data, it's the partition where apps are installed and where they keep their private data.

Also /storage/sdcard0 could be part of internal phone memory, called PHONE STORAGE it's an emulated sdcard (I can't tell if in your case that's emulated sdcard or real)

To make a raw backup of your data you need to know which block contains that partition, you can check it with this command:

cat /proc/emmc


Result should contain lines like this:

emmc_p7: 001a4c00 00300000 "usrdata"
emmc_p8: 004a4c00 0358dd00 "fat"


This gives you partition number p7 , now you can use this command to list blocks:

 cat /proc/partitions


Result should contain:

  179        7    1572864 mmcblk0p7
  179        8   28077696 mmcblk0p8


In this case to backup /data aka emmc@usrdata contained in mmcblk0p7 block you can use this command:

dd if=/dev/block/mmcblk0p7 of=/storage/sdcard0/usrdata.img


Supposing sdcard0 is working properly and there is enough space.
After that usrdata.img can be mounted in a linux box with:

sudo mount -t ext4 -o loop usrdata.img ./folder


P.S.
You might check how to use adb so you can open a console on your computer and issue commands to your phone connected with usb.