There are a few options. In your position, I would set up a new 14 system and use this script to migrate your settings over to the new install:
https://wiki.freepbx.org/display/PPS/Elastix+and+PBXinaFlash+to+FreePBX+Distro+Conversion+Tool
You could also set up a new 13 system and restore a backup of your old system and then update the new system using the link provided above.
Edit 3 months later - now that FreePBX 15 is more mature, I would recommend setting up a new 15 system and restoring a backup from the 13 (or earlier) system. FreePBX 15 is the first version to support restores from legacy versions.