At this point after seeing your external hard drive in Disk Management, I recommend that you do the following.
Download the HDD LLF Low Level Format Tool ver 4.25 ( Windows executable - needs no installation) HDDGURU: HDD LLF Low Level Format Tool
Click (double click) on it and run. Choose your external hard drive
and low level format it. ( This may take quite sometime but you can see the progress in the bar)
When done your ext. hard drive would have been initialised to the factory condition and you will be starting with a clean slate.
Now partition/format it to exFat with Disk Management. Assign drive letters when done if necessary.
Keep us posted.