External Harddrive is showing in System Information but not Disk Utility
So I know this was asked a very long time ago but for the sake of people landing on this page, here's what I know:

If it shows up in system utility and your drive is spinning (as mine is), that means your hard drive enclosure is functioning and the logic board inside is working as well. However, if it's not showing up in the disk utility then there is still an internal problem with the hard drive. Since it is at least partially functioning, it may be possible for a professional to be able to recover some or all of the data from the drive but you'll probably need to invest in a new one for future use. Sorry.