MacOS – USB LG Drive Not seen

If your USB hard drive is the bus-powered variety (that is, you don't plug it into the wall for power), then it is possible that it is requiring too much startup current to run on one of your computers.

Some computers are pickier than others about how much current a device can draw, and over what period.

You might try a cable like this:

Basically, you can use power from two USB ports, instead of just one.

If your hard drive has a jack for a power adapter, use that instead.

Have you opened Disk Utility and tried to format it already? Sometimes a drive will not appear on the desktop, but will appear in Disk Utility.

I've had windows drives show up sometimes, and not other times. What you could do to make it more likely to show up is go to an available (hopefully not too difficult) windows machine and reformat the drive as a FAT/MS-DOS drive (don't do quick-format). This should be easier for the mac to see.

Once you can see the blank FAT formatted drive, open Disk Utility and then select it on the left sidebar and erase it again as a "Mac OS Extended (Journaled)" (HFS+) format.

There are other methods like using an emulation environment like Parallels Desktop (IMHO bad SW company), VMWare Fusion (my choice), or VirtualBox (free) (all of these require a windows install disc); or you could even try using programs like MacFuse or NTFS-3G, Tuxera, etc., to mount windows (NTFS) drives directly in the Finder. But unless a mac you can find has one of these solutions, it's probably not worth it to go through the trouble just to erase one drive.

Lastly, I've also had some external USB enclosures not show up on some versions of OS X! So the cheapy enclosure you got just might not work with your installation anyway?

Details that might be helpful for potential helpers:
HD interface PATA/ATA/IDE or SATA?
OS X Version?
iMac model year or identifier?
Enclosure is assumed to be USB 2.0 high speed plugged into built-in port on iMac. Correct if wrong.