Starting at the beginning, have you tried plugging something else into the wall socket that powers your external drive, just to check that the fault isn't in there?
You've tried power cables connecting the wall socket to the power port on the outside of the caddy, but have you checked that the drive itself is properly connected to the power plug inside the caddy?
If none of the above works, then I think my next move would be to install the drive as a slave inside the computer, to see whether it works like that.
If it's still kaput connected like that, then I suspect that it is indeed kaput.
If the drive is not functioning, then I'm afraid that recovering data from it will be the job of a specialist company. Not cheap.