First, make sure it is powered up. If it gets power from the USB port, make sure the port supplies enough current to it (some ports do, some don't, even on the same PC).
Then, see if the drive appears in Disk Management (Admin Tools). If it does, it may need initializing first (although that would entail losing all the data from it).
Before giving up on data, try to remove the HDD from the enclosure (since the fault could lay within the enclosure, not the disk) and connect the HDD using a different method (external dock, internal mount, etc).