several system files have been corrupted due to usb problems
This may or may not be a significant problem for you.
To decrypt the contents of an encrypted home, Ubuntu normally needs not only the login password but also a "mount passphrase" - a secret, long secure string that was probably generated automatically for you at the time of setting up your encrypted home.
If your system can boot normally it will already have the mount passphrase in a "wrapped" format stored on the drive, and will only need your login password to complete the decryption. However if your system becomes corrupted and you need to recover files from another OS (such as a Live CD) then you will need this mount passphrase as well as your login password. So if this mount passphrase is part of your system that has become corrupt, and you didn't take a backup of it, you may be completely out of luck.
Nonetheless, it's possible that the wrapped version of the passphrase may still be on your drive somewhere an will have survived corruption, in which case you're in luck.
This page details how to recover files on an encrypted home from an Ubuntu Live CD.
It involves using a helper tool:
This will try to find all the encrypted home directories on the system and their corresponding wrapped mount passphrases. If it does, all you will need to decrypt them will then be your login password.
If it doesn't find a surviving wrapped mount passphrase, and you don't have a backup of it, you are likely to be out of luck.
It it does work, it will temporarily mount the decrypted contents into a mount point inside /tmp. Then you should copy the decrypted files from there onto another device. See the whole article for more information.
Note: to anybody wanting avoid this problem, if you set up an encrypted home directory make sure you save a backup of the mount passphrase somewhere. You may be prompted to do this when you first set up the encrypted home, but if not you can access it later - after you've successfully logged in - with the command
ecryptfs-unwrap-passphrase. This will only work if you've logged in normally on the system - that is, it won't work when you need to recover as in this OP's situation.