This is a really crappy bug, and I don't know of an easy way to recover. If you don't feel able to carry out these instructions, get someone more experienced to help you. One option is to make a "Genius" appointment at an Apple Store.
You need at least two complete, independent backups of all data before proceeding. There are ways to back up a computer that isn't fully functional. Ask if you need guidance.
Start up in Recovery mode by holding down the key combination command-R at the startup chime. Release the keys when you see a spinning globe.
When the OS X Utilities window appears, select
Utilities ▹ Terminal
from the menu bar at the top of the screen—not from any of the items in the OS X Utilities window.
Follow the procedure in this thread to erase the FileVault volume. The long string of letters, numbers, and dashes that you will have to enter will be different in your case. Copy and paste it from the Terminal window into the command.
This operation will remove all data from the volume, so you had better be sure of your backups.
Quit Disk Utility. You should then be able to restore the data from a backup in the main screen.