Welcome to just answer,
If you were able to see the files on a regular pc, I would copy them to your computer hard drive, format the drive then copy them back. I would curious to what file extensions they are.
Try this and let me know the results.
Thanks for your clarification. Can you tell me who is the hard drive manufacturer? I would recommend purchasing a similar drive and install it on the system and see if it will work.
The hard drives on these systems are formated differently than the hard drive on the computer. If you can find the USB to hard drive connecting tool, you can try. But I am not sure whether this will work without formatting it.
I was actually thinking mac might also that better. Do you have linux?
You can try any thino as long as you do not format
You can find one here
When you installed the external USB drive on the computer, did you check on device manager to see if windows see it as a device on USB port?
My last suggestion is, to purchase another drive and format it to be used on the current system. Keep the old one until you can find a way to recover the files.