It could be that the external enclosure is bad. In which case, you could take it out of the enclosure and put it in the PC case and it would work.
I've actually had an iomega external HDD do that to me before. I couldn't figure out what the hell was the issue, I finally tried taking it out of the enclosure and putting it in a PC and it worked fine. I was so pissed that I calmly took the faulty enclosure to the back, 2nd story door, and chucked it at the dumpster. It actually landed on the edge of the metal dumpster, causing lots of plastic to break and fly everywhere, but most of it went in the dumpster, and I felt MUCH better. lol.