Because the question itself is not 100% clear, this is what I was able to make of it so far.
All of the sudden, when you go to the start menu, and press shutdown, and you get the shutdown box, you choose one of the options, and press OK, but nothing happens.
My first suggestion is to try again with Notepad open to see if at least notepad is being closed or not.
This will indicate if shutdown is being blocked by a program that is not responding and keeps the system active, and/or if a system component is damaged which prevents you to do this.
My recommendation is to hold the power button for 5 seconds until the PC is fully powered off. Unplug the power cord and press the power button once to ensure that all power in the system is gone. Wait 5 seconds and plug in the power cord.
Start up your system and check if the shutdown options work now. If so, it was a program/service that crashed. If this happens again, you should look into what program is hanging and why it does. If not, it was just an event happening once.
If you can't shutdown at this time though, a system component is corrupted.
Start a command prompt and type in:
sfc /scannow. This command will check all system components and fixes any issues there may be.