As i told you on the IRC chan, It is advised to install from scratch after backing up your data. It is a major release, a lot has changed in the core. Maybe you can borrow an hard disk from a friend of yours, just to copy your data and then restore them. But next time split your drive in partitions, so you can use a system partition with about 10Gb, it should be enough, and the remaining part will be used as data partition. Or you can also have a separate partition to mount as /home. It's up to you, but please organize your disk in a maintainable way.
You can try to upgrade the Ubuntu version to 14.04 from the Update Manager, and then import BackBox 4 repos, but it's not guaranteed it will work, and i think we won't offer support in such a situation, where breakages are likely and no one can verify them.

Have fun!