That's not exactly what I meant, since Restore from Time Machine Backup will simply reinstall everything that was previously backed up, including the problem. What I meant by migrate your old account from the Time Machine backup was to complete an initial setup of a new Mavericks installation, followed by using Migration Assistant to migrate your essential apps, documents, music, and other files.
If you elect to do that I recommend you initially set up a brand new account using a temporary, "throwaway" name different from the one you have always used. That account will contain nothing other than the native OS X apps. Make sure that account works acceptably (it will), then use Migration Assistant in your Utilities folder to migrate the essential files in your normal User account from the Time Machine backup. You can then log out of the temporary account, log in to your real account, verify it works acceptably (it will), and then use System Preferences > Users & Groups to delete the "throwaway".
The only mystery will be the reason this happened to begin with, but if you're more interested in restoring your Mac to operation it may be the better alternative.