Forget what you've been told about using DOS for drive letter assigment, that's wrong. Chances are the 500GB partition will be an NTFS one, and DOS can't do anything with NTFS partitions.
Assigning a drive letter is done in Windows, using Disk Management in fact. Obviously that can't be done in your case since Windows is not seeing it.
It's possible the drive has failed and no longer any use, or the converter board (converts SATA to USB) has failed inside the drive enclosure. That's very common with external drives, and it means the drive itself could be perfectly alright in that case. You'll need to crack open the enclosure, remove the drive & fit it inside a third-party enclosure.