Hi, TM fails big time as a trustworty backup app.
You may have used TM to replace an with an OS that won''t run on a newer Mac.
Bootup holding CMD+r, or the Option/alt key to boot from the Restore partition & use Disk Utility from there to Repair the Disk, then Repair Permissions.
If that doesn't help Reinstall the OS.
Reset OS X Password Without an OS X CD...
Starts up like the first time you buy a new Mac, but after filling in all that info again, you should have access to the computer and the other Users & files will still be there... give the new User a different name than an existing one.