I have to do what I didn't want to do in the first place. Waste a DVD to burn Linux Mint 17. Copy my files onto an external HDD. And install 17.
Can I just say that if you have to go down this road that it may be advisable to re-partition your drive to have three partitions; "/", "/usr", and "/home".
I've recently had to rebuild my system due to a Mobo failure, it was running Ubuntu 10.04 lts. I tried the new 14.04 but had problems and didn't like the Unity desktop. I've now run a fresh install of Mint 17 with the partitions as above, specifying "Don't format" the /home partition.
It picked up all my Firefox bookmarks, Thunderbird worked straight off with all my emails and contacts intact (OK, I did have to pull in the upgrades before it could be selected from the desktop.) I also loaded up KWalletManager and it picked up all the passwords I thought I'd lost. Very impressed!
I'd moved all the .config files in /home/<myname> to a temp folder in /home (well, as many as I could!)
Another benefit of having separate partitions is that if the drive has a head crash and you can't boot from it, in all probability you should be able to mount the /home partition with a Live CD and retrieve your data. The crash is likely to be on a system partition as it's accessed more. (The can't-boot thing would be a hint)