Here's a link I came across for anyone interested:
It goes over the symptoms of hard drive problems including "not seen." It also references other stuff that may be of use to you.
Regarding compatibility, theoretically any USB or FireWire drive should be "plug and play" unless you ended up installing a third party vendor set of device drivers etc. that aren't compatible. This was (and might still be) a problem with some of the Seagate external drives when using Mountain Lion. I know Seagate offered some updated software kits to fix at least some of the problems.
As Eustace said, some external USB drives need adequate power, and if the USB port can't provide it, on some units it will "sort of" look like its on but it actually isn't. I bought a cheap USB enclosure and it comes with two cables because it needs two ports. WIthout using 2 ports it will look like it's on but it's not really functional...then again it cost 5 bucks so I guess I shouldn't be too surprise! ;-)
Thank you very much - great link. Just skimmed it, but have it saved for later.
For many years now I have used a powered usb hub with each of my Macs. The hub is plugged into the wall for power, and connected to the Mac for data. All USB devices are plugged into the hub for power and data flows through the hub.
I first did this because it such was a **** nuisance to keep reaching behind a huge tower to find an empty usb port. My main computer's usb hub has a printer, a scanner, a keyboard, a mouse and two camera cables connected all the time.