If no configuration changes have been applied I would suspect of a virus infection. Make sure you have an up-to-date antivirus and perform a full scan in safe mode.
If the computer is clean, take a look at this article, which offers a couple possible solutions.
That’s an excellent article. You might also want to check that your security suite isn’t managing the firewall settings. In particular, I know that Norton Internet Security and Symantec Endpoint Protection both manage the Windows firewall as part of their configuration and this also causes the option to be greyed out.