Hi Mike!
Does HDD spin or not
?If it's spining
try to freeze your HDD in sealed plastic bag for one hour and then try if you can do one more back up
.If it's working just copy/paste files to your PC.If it's not working get some recovery program like Acronis or Recovery manager
.There are some free programs like
http://www.pcinspector.de/Sites/file...htm?language=1 
.If using any program install your failed ext. HDD as secondary HDD in your PC and try recovery/backup with program you installed.
Hope you will have luck