Encrypted hard disk data recovery
There are two possibilities of encryption within Ubuntu.
- Full disk encryption
It means that the whole disk is encrypted. Immediately after starting (right after booting the kernel) you are prompted for a password. It looks like this: http://imacify.com/wp-content/uploads/2013/08/Ubuntu-FDD-lock-Screen.jpeg
This does not seem your case, because your problem happens later in the booting sequence.
Anyway, this guide shows you how to access an encrypted volume using a Ubuntu Live CD or USB stick. You should be able to recover some data and copy them over to another disk. Good luck :)
https://alvinabad.wordpress.com/2012/09/22/how-to-recover-a-luks-encrypted-disk/
- Home folder encryption
In this case, home partitions are encrypted on a per-user basis.
Here are a few resources for you:
http://www.howtogeek.com/116297/how-to-recover-an-encrypted-home-directory-on-ubuntu/
https://help.ubuntu.com/community/EncryptedPrivateDirectory
You should try to recover your data first. But I also think that it should not be too hard to restore functionality to that box.