Do you mean you have a SATA drive or PATA IDE drive (regular HDD) that has been placed in an external enclosure, like a Lantex NexStar, or Antec, with a USB 2 connector?
If so, it sounds elementary but that external drive needs external power. It does not get its power source from the USB cable. Make sure that the power light on the enclosure is on, and you can hear the HDD spin up.
Also change out the USB cord for thoroughness.
Then with your computer off, and the USB drive off, connect the USB cord. Then boot up your computer.
After it is on the desktop, turn on the USB enclosure. See if you get a beep that your OS recognized the USB drive, and it should be visible in Windows Explorer.
There is always the possibility that the HDD/USB interface connector inside the case is not tight, so removing the hard drive, and reinserting it into the internal connector would be something to consider.