You can find testing tools for hard drives in manufacturer's web site.
This can tell you if the drive is good or no.
There are commercial testing tools too.
I would suggest the following steps, with free tools or with some very basic possibilities of your computer.
1. Be sure that the BIOS detects the hard drive. For this, connect the hard drive to the computer, turn the enclosure's power switch on and then turn the computer on. Look carefully the P.O.S.T. screens. Normally, the BIOS detects that a hard drive is connected to a USB or Firewire or e-SATA port, and displays its manufacturer's code.
In case of problem, just a hard drive can be reported but no further details.
Please, note that a good unpartitioned / unformatted drive can take some seconds to be detected, but if this becomes too long (more than say 30 seconds), something goes wrong.
A defective drive can be quite long at this phase, or even not detected at all.
2. From within mswindows, you can run the disk management. There, you have to find the hard drive shown in the lower part of the screen, but nothing in the upper part (if there are no mounted partitions). Sometimes, you have to select Refresh from the menu, if not displayed repeat 1-2 minutes later. Furthermore, sometimes you have to reboot and retry. Note that this "random" behaviour can be sign of problem in the drive (or the enclosure, don't forget it too, so check that it works with another drive 
).
3. You can boot the computer from the GParted live (CD or USB). GParted displays every device that belongs to the hard drive "family", i.e SATA/IDE/SAS/SCSI hard drives, external hard drives, as well as flash drives. A defective device is much longer to detect, is wrongly detected or isn't detected at all.
You can open the terminal window and run the command dmesg, This displays every system message related to the boot process and problems in the hardware detection and configuration.
4. If GParted detects well the drive, you can create a new partition table (msdos type). Be careful, to select the good drive, because this deletes the previous partition table and partition definitions.
After that, you can create your partition in the entire disk space, using the default options (1 MiB left before the partition, MiB alignment) and selecting to format it as ntfs. This normally takes just a few seconds. It doesn't do a full surface check, nevertheless you can do it later with the chkdsk /r command from the dos window in windows. It is quite long for a USB2 interface.
5. If the drive seems good but the problems insist, you can try to erase its initial part that eventually confuses the windows registry. To do this, you can run the following command from the command line, running GParted live or any Linux distribution:
sudo dd if=/dev/zero of=/dev/sdx bs=1M count=1024
where /dev/sdx is the device name for the hard drive in question (usually something like /dev/sdb, /dev/sdc ... for an external drive. Be extremely careful for this, because there is no undo. In case of doubt, you could remove any other hard drive from the computer, to be sure that you can't go wrong!
This will erase the first gigabyte of your hard drive, including the old partition table and partition boot sector. So, you can work on an "empty" drive.
If the enclosure is the problem, you can try to partition the drive by connecting it directly to a SATA port.
*** It is highly recommended to backup any important files before doing resize/move operations. ***