It looks like we are going to have to do a repair install on the system. The repair install won't delete your data, installed programs, personal information, or settings. It just repairs the operating system!
I would still suggest backing up your data just in case something goes wrong. There are some suggestions here on how you can backup your data.
The page here gives you some more information about a repair install and instructions on how to do one.
Let me know how you get on!