It sounds like you're using the "legacy" (pre-Lion) version of FileVault, and the disk image file on which your home folder is stored is corrupt.
This condition is quite difficult and time-consuming to recover from. If the procedure suggested here is too hard, get help from someone more experienced. One option is to make a "Genius" appointment at an Apple Store.
Legacy FileVault is obsolete and should not be used under OS X 10.7 or later.
If you have another user account with administrator status and can do so, log in to it and skip to Step 4.
Step 1
Start up in Recovery mode. The OS X Utilities screen will appear.
Step 2
Select
Utilities ▹ Terminal
from the menu bar. In the window that opens, type this:
resetp
Press the tab key. The partial command you typed will automatically be completed to this:
resetpassword
Press return. A Reset Password window opens. Select your startup volume if not already selected. Pull down the menu labeled Select the user account and select
System Administrator (root)
Follow the prompts to set a password. It's safest to choose a password that includes only the characters a-z, A-Z, and 0-9.
Select
▹ Restart
from the menu bar.
Step 3
At the login screen, click Other... Enter "root" (without the quotes) in the Name field, and enter the password you set in Step 4 in the Password field. You should now be logged in. Do nothing while logged in as root except as indicated below.
Open the Users & Groups preference pane. Create a new user and check the box marked
Allow user to administer this computer
Restart and log in as the new user.
Step 4
Load this web page in Safari.
Triple-click anywhere in the line below on this page to select it:
sudo dscl . -delete users/fubar HomeDirectory
Copy the selected text to the Clipboard by pressing the key combination command-C.
Launch the TextEdit application. Paste into the window by pressing command-V. Double-click the word "fubar" and type the short name of the affected FileVault user.
To be clear, the command line above is just an example. You must edit it before using it.
Triple-click the edited line and again copy to the Clipboard.
Launch the built-in Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
Paste into the Terminal window. When prompted, enter the password of the user you're logged in as. Nothing will be displayed when you type it. Type carefully and then press return.
Step 5
You should now be able to log out and log in as the FileVault user. Your files still won't be available. FileVault is inactive.
Locate the disk image file named "fubar.sparsebundle" or "fubar.sparseimage" at the top level of your home folder. Again, these are only examples, not the actual name of the file you're looking for. Substitute the short user name for "fubar".
Step 6
Try to open the file. If it won't open, try to repair it in Disk Utility. If it still won't open, restore it from your most recent backup. Keep trying older backups until you find one that works. If you don't have a backup, the data is lost, perhaps beyond any hope of recovery. There's a slight chance that you might be able to repair the disk image using an expensive third-party application called "Disk Warrior." If possible, go to a "Genius Bar" where the software is available for use by the "Geniuses" at no charge.
Step 7
Copy the files from the mounted disk image to the corresponding subfolders of your home folder. The Library folder is invisible in the Finder. Open it by holding down the option key and selecting
Go ▹ Library
from the Finder menu bar. Open the copy on the disk image by selecting
Go ▹ Go to Folder
and entering something like
/Volumes/fubar/Library
in the text box that opens. Again, substitute the correct name for "fubar".
Log out and log back in.
If there isn't enough disk space available to complete this step, unmount the disk image, copy the disk image file to an external storage device, delete the original, and try again.
Step 8
Back up all data, then delete the disk image file.
Step 9
Delete the user you created in Step 3, if applicable.
Step 10 (optional, but recommended)
Follow the instructions in this support article under the heading "Disable the root user."