Is you drive very small and has only one cable, the USB connection ? These hard drives are powered from the USB port. It may be that your USB port cannot supply enough power to it.
You didn't say whether your computer is a laptop or a desktop. If you have a laptop the you may have to get a powered USB hub
. If you have a desktop then you could use either a powered hub or a PCI USB adapter card
Keep in mind that your problem may or may not be a power issue, but these kinds of drives do often have this problem.
Another thought to consider is that a USB flash drives
(aka pen drive) have come down in price considerably. I just bought a 1GB for less than $45. Now its going for less than $35, delivered ! This one is a particularly fast, durable and inexpensive. They use very little power, too.