Well as you didnt say what Operating System you are using, I willl have a guess at XP?

One of the reasons you cant access it is beacause you have your old Operating System installed on it and you need to have the right permissions to view the file system and certain folders on the drive, (benifits of NTFS). If you dig around you will find that there will be other files on it you wont be allowed to open.

Some steps you can try to help are:

Make the root of the drive "Shared" and see if you can access it then - it may ask you for a username & password
or
Just see if you can make the My Documents folder shared
or
See if you can drag it into the shared documents folder

Can you copy and paste/send to, to your new hard drive

Install an OS that does not conform to the NTFS rules, i.e Linux then boot into Linux and you will have full and unrestricted access to your windows partition.

Or as you said the hard drive failed it is feasable that there is some physical damage to the hard drive and thats why you cant access the folder. Feasable but unlikley to just affect one folder, try running a surface scan on the hard drive just to see if there is damage.