Impossible with the standard libs alone. In the standard lib, once you poll for input, it will wait indefinitely until the user responds. You can't tell it to stop waiting after X amount of time.
To do this, you'd either have to get into platform specific console I/O, use a 3rd party console I/O lib, or make the program multithreaded (ew).
What Disch said. Personally, I would go for multi-threading. Threads are simple to create, and easy to understand. As for the alarm, including the <Windows.h> header will give you access to Beep( ).
Making a threaded application is not hard. As for making it thread safe...
You should give up the console and try your program with SFML. The console isn't great for this kind of thing IMO. If you use a multimedia library, you don't need multiple threads for the timing business, though getting user input might be more work, but not conceptually difficult.
(PS: As for the SFML input tutorial videos I promised you, I shall be uploading them eventually, I just ran into some delays in the mean time :p)