What part about a live CD didn't work? Are you able to run the PC on CD? Based upon the information in your other thread, especially the part where you state that Windows in non safe mode and Ubuntu are both failing, I agree that you have a hardware problem with the machine.
If you are able to get a command prompt for login (CTRL-ALT-F1), you may be able to do what you need to do. One advantage of the live CD that you may not have is the ability to elevate to root privilege which may be required to "mount" drives. With the encrypted home partition, your home folder is stored as a file in another part of the file system in encrypted format. When you login, this file is supposed to auto mount to your home folder location. Something clearly has gone wrong and you are not able to fully login, mount it, etc.
Since you can get to the drive, I would suggest that you do the following items:
1) use fdisk -l to see what partitions it is showing. Hopefully you see at least one "Linux" partition. If you see more, your /home folder should be on one of these.
2) once you determine what partitions you have, you need to locate the .Private folder. Mount the partition and use:
sudo find / -type d -iname '.Private' 2>/dev/null
3) you need to find the keyring key
sudo ecryptfs-add-passphrase --fnek
, which requires the MOUNT passphrase you obtained.
4) next you need to mount your encrypted home directory (mount -t ecryptfs, for mount type encrypted file system) to a desired location. You will need the pass phrase again. You will also be prompted for a few parameters. I would follow what is in the how to document.
Whether or not you are able to do this with the username@username prompt will depend upon whether you can see the partition with /home and whether or not you can gain sufficient privilege to mount the volumes. If your lucky, sudo will work for you.