Your first problem is that your PC has a 32-bit LBA limitation. This is the reason that DMDE is detecting a reduced capacity of 1.8TB instead of 4TB. You need to install the latest SATA driver.
The good news is that your My Book (?) is not encrypted (is it an Elements model, or are you in a country where encryption is illegal?). If you purchase a replacement USB-SATA bridge board, I have no idea if it will play with your non-encrypted HDD. However, because there is no encryption, your HDD should work with any USB-SATA adapter/dock/enclosure which is configured with a 4KB sector size.
In any case, after you install the latest SATA driver, you can double-click the NTFS[4K] volume and expand the Root. Hopefully you will now see your file/folder structure. The free version of DMDE will allow you to recover a limited number of files. I don't know whether Recuva will be able to see them, but you could try.
Alternatively, there is a way to "fix" your bridge PCB, assuming that the damage is confined to the 5V regulator. All you would need to do would be to snip the pins of the regulator, remove it, and then run separate +12V, +5V and Gnd wires from your PC's PSU. But that's something that requires a little technical ability.
BTW, you can capture a screenshot to the clipboard using the PrtSc key on your keyboard. Then paste the clipboard contents (Ctrl V) into your preferred image editor.