10.7.5 update failed. Cannot login now

Question

I recently updated to 10.7.5 from 10.7.4 on my Macbook 4,1 (2008) and during the update, there was an unexpected error and it just restarted itself. Upon logging in, it was stuck on the gray screen with the apple logo and spinning wheel. I left it on thinking it was going to revert back or something but it has been stuck in like that for 4+ hours. I decided to try to reboot it and try to fix it. I still cannot login but I am able to use the recovery options. I would prefer not to just reformat it (as I don't have a time machine backup) but I will if there is no other solutions.
It is worth noting that I am unable to get into Safe Mode due to FileVault being on. Quite unforunate
Using DiskUtility, I am unable to verify or repair the disk. It gives me the error message "invalid node structure" and asks me to repair and when I attempt to repair it spits out "invalid volume header @ 0 : incorrect block type"
Here is what happens when I try to use terminal to repair it after decrypting.
#diskutil repairVolume disk14*
Started file system repair on disk14 on Mac OS X
Checking storage system
Checking volume
disk0s2: Scan for Vlume Headers
disk0s2: Scan for Disk Labels
Logical Volume Group 8A4F60D2-178D-4256-997E-A001010288A5 spans 1 device
Logical Volume Group has a 16MB Metdata VOlume with double redundancy
Start scanning metadata for a valid checkpoint
Load and verify Segement Headers
Load and verify Checkpoint Payload
Load and verify Transaction Segement
Load and verify Transaction Segement
Load and verify Transaction Segement
Incorporate 2 newer non-checkpoitn transactions
Load and verify Virtual Address Table
Load and verify Segment usage Table
Load and verify Metdata Superblock
Load and verify Logical VOlumes B-Trees
Logical Volume
contains 1 Logical Volumes
Load and verify D6933BD7-D715-4869-8EB4-59C598F2207B
Load and verify 64B575DE7EB2-4ED7-89F0-CEACF08E6F1E
Load and verify Freespace summary
Load and verify Block accounting
Load and verify Segment Cleaning
Newest transaction commit checkpoint is valid
The volume 8A4F60D2-178D-4256-997E-A001010288A5 appears to be OK
Checking file system
Checking Journaled HFS Plus volume
Checking extents overflow file
Checking catalog file
Invalid node structure
The volume Mac OS X could not be verified completely
Volume repair complete
Updating boot support partitions for the volume as required
Error: -69845: File system verify or repair failed
Underlying error: 8: POSIX reports: Exec format error
*("diskutil list" reveals that disk3 to disk13 are random disks named "untitled" that are mostly 524.3KB in size, with a few ranging from 1.0 - 6.3MB. Not really sure why)

Answer 1

I'm guessing your system had damage before the update was installed. The only hope, in my opinion, for Invalid Node Structure repair is the following....
If Disk Utility can't fix it, you'll need a more robust utility to repair it.
I would recommend DiskWarrior. It is the best at directory repairs. It rebuilds then actually replaces your old directory. I feel every Mac owner should have a copy.  It also has File System repair now and hard drive S.M.A.R.T. diagnostics.
Make sure you get the disk so you can boot up on it to run repairs. You can also install it on another drive and run it from there to repair this one. DW works faster that way. But sometimes a badly damaged system can be deemed unrepairable by the installed version, but if booted and repaired from the DW disk it may be repairable. This has happened to me.
I use DW once a month to try and catch errors in my system from getting too far out of hand. It has repaired every little and big issue I have ever had with my  three Macs.
Good Luck!  DALE