There is no reason why a drive would be present in device manager (and presumably the BIOS) and not show up in disk management, unless it was somehow inaccessible. I believe you may have a soft-failure of the drive here, which is usually due to some kind of electromagnetic shock to the controller or damage like that. Ironically, hard drives rarely respond as though they are governed by the laws of logic, so shelve it for a few days and see if it responds better. Another thing you could try is to put it in the fridge for a few hours - sounds ridiculous but when people attempt to rescue data from hard drives this is often a good way to access data while you can.
I can't guarantee success and in all likelihood you'll never be able to access the drive again. To check and make absolutely sure, you could try a different USB connection cable between the drive and the computer in case one of the data loops has been damaged, but its much less likely than a soft failure.