Is the drive formatted? A non-formatted drive will never show in My Computer/Explorer, but will be properly reflected in Device Manager and Disk Management.
Go to Disk Management (Start/Run...type diskmgmt.msc and hit Enter) and see if the drive is reflected there as unpartitioned, unformatted.
If it is, format it and upon completion of same, it will show up in My Computer/Explorer view.
You might also check whether you have to use FAT32 or NTFS with the enclosure...some are picky.
You might also check the jumper setting which may be required for the enclosure.