Using disk utility, I was erasing and re-formatting to FAT. During that process, the usb cable was removed. Now, the hard drive will not format. When recognizing the hard drive, a window shows up stating "The disk you inserted was not readable by this computer" with the options to "initialize; ignore; eject." "Initialize" does not seem to do anything. Disk Utility shows the physical drive, but no sub folder (volume?) When attempting to erase and create a new partition, I get an error. The disk was already empty, so I'm not worried about retrieving files, but is the drive itself physically damaged?
You could try overwriting the partition table with zeros. To do so, enter
sudo dd if=/dev/zero of=/dev/disk3 bs=1m count=1 in a Terminal window. This will overwrite the first megabyte of the drive with zeros, which will include (and thus erase) the partition table (or its remnants). Remove and re-insert the drive; if everything goes well it will tell you that the disk was not readable and it'll offer to initialise the disk. (I tried this with an old USB stick a minute ago and it worked fine.)