EDIT: I see there is another question already on this issue. It seems you will just have to keep emailing Facebook about it and they will fix your account.
I would say your system has been compromised. You may have some sort of virus that could have stolen your login details to various websites. Most likely the hacker could have logged onto your facebook account and changed the password. The virus may still be functioning. I suggest checking running processes and looking for suspicious ones.
If you have a anti virus program, do a full scan. If you do not then I suggest getting Malware Bytes. It's free to perform a scan and such, and I find it works good.
Next I would naviagte to your hosts file. (Not hosts.bak) and open it. You can find the hosts file in the following location on a Windows computer:
C:\Windows\System32\drivers\etc
Make sure there is nothing that looks fishy. Microsoft has examples of what various host files look like for different versions of Windows. You can see these examples here: http://support.microsoft.com/kb/972034
If you find extra lines in there that the examples don't show then it's a pretty good indicator you are infected.
Good luck!