Do other USB devices work fine, keyboard, mouse, flash drives? If this is a usb powered enclosure, see if it will work with external power to it (that may not have been included in your purchase though). Another thing to try, some places have dual-ended usb cables to draw more power to the device, try that. Your computer may not be sending enough power to the usb ports to power the hard drive.
Try to listen closely to the drive, see if it's making faint clicks when plugged in, that is one of the signs of not enough power.