External Hard Disc won't mount - Partition Map error.  Can't repair with Disk Utility

Happy New Year all and thanks in advance for any support/advise.
I have some important data on an external drive that does not seem to want to mount.  The drive is a 500 GB Seagate connected via USB.  I am currently on an iMac 3.06 GHz Intel Core 2 Duo running Yosemity 10.10.1
What I've tried:
Multiple computers - connected the drive to various apple computers with the same result.
New enclosure:  I have removed the actual HD from the enclosure and connected it using a new one.
Disk Utility:  Verifying Disc reports the following error:  'Error: Partition map check failed because no slices were found.'  Screenshot below:
I have searched this and other forums and run a few commands in Terminal that seem relevant to the issue, but am out of my depth in terms of interpreting the results.  Thank again for your attention!!!
Commands run in Terminal:
diskutil list
diskutil cs list
mount
diskutil info disk1
Full Results pasted below:
diskutil list...
Ethan-Smiths-iMac:~ Ethan$ diskutil list
/dev/disk0
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *1.0 TB     disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:                  Apple_HFS Macintosh HD            999.3 GB   disk0s2
   3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3
/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *500.1 GB   disk1
   1:         Microsoft Reserved                         134.2 MB   disk1s1
diskutil cs list...
Ethan-Smiths-iMac:~ Ethan$ diskutil cs list
No CoreStorage logical volume groups found
mount...
Ethan-Smiths-iMac:~ Ethan$ mount
/dev/disk0s2 on / (hfs, local, journaled)
devfs on /dev (devfs, local, nobrowse)
map -hosts on /net (autofs, nosuid, automounted, nobrowse)
map auto_home on /home (autofs, automounted, nobrowse)
diskutil info disk1...
Ethan-Smiths-iMac:~ Ethan$ diskutil info disk1
   Device Identifier:        disk1
   Device Node:              /dev/disk1
   Part of Whole:            disk1
   Device / Media Name:      ST950032 5AS Media
   Volume Name:              Not applicable (no file system)
   Mounted:                  Not applicable (no file system)
   File System:              None
   Content (IOContent):      GUID_partition_scheme
   OS Can Be Installed:      No
   Media Type:               Generic
   Protocol:                 USB
   SMART Status:             Not Supported
   Total Size:               500.1 GB (500107862016 Bytes) (exactly 976773168 512-Byte-Units)
   Volume Free Space:        Not applicable (no file system)
   Device Block Size:        512 Bytes
   Read-Only Media:          No
   Read-Only Volume:         Not applicable (no file system)
   Ejectable:                Yes
   Whole:                    Yes
   Internal:                 No
   OS 9 Drivers:             No
   Low Level Format:         Not supported

Select the disk1s1 volume under the main drive entry, then click on the Mount icon in the Disk Utility toolbar if it goes active and see if a volume then mounts on your Desktop. If it does not, then you need to reformat the drive. And, you cannot access the volume in order to copy your data somewhere else. If you are willing to spend money on the problem, then you can always try using a software recovery utility:
General File Recovery
If you stop using the drive it's possible to recover deleted files that have not been overwritten by using recovery software such as MAC Data Recovery, Data Rescue II, File Salvage or TechTool Pro.  Each of the preceding come on bootable CDs to enable usage without risk of writing more data to the hard drive.  Two free alternatives are Disk Drill and TestDisk.  Look for them and demos at MacUpdate or CNET Downloads. Recovery software usually provide trial versions that enable you to determine if the software would help before actually paying for it. Beyond this or if the drive has completely failed, then you would need to send the drive to a recovery service which is very expensive.
The longer the hard drive remains in use and data are written to it, the greater the risk your deleted files will be overwritten.
Also visit The XLab FAQs and read the FAQ on Data Recovery.

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    http://discussions.apple.com/thread.jspa?messageID=11073082#11073082

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