Apple all in one computer's keyboard not working

I wasn't sure what board to put this under.

My wife's Apple All-In-One computer's keyboard keeps failing. It's a wired keyboard... she was having trouble with her wireless keyboard not working, so she bought one with a wire. What happens is this: She turns on the PC, and the keyboard does not work, none of the keys respond. After many attempts rebooting, shutting off, turning on, plugging it into a different slot, eventually, the keyboard works again. This is not a case of certain keys not working... either all of them work or none of them work. Then, after much frustration getting it to work, sometimes spending hours struggling with it, the next time she comes to the computer, it has automatically shut off for some reason, and the same thing happens all over again. We brought it to the Apple Store "Geniuses," but of course, that was one of the times that shutting it off and on and replugging it in actually worked, and they said, there's no problem. And, of course, when we got home again, it didn't work again and we had to keep turning it off and on and switching which slot it's plugged in until it eventually works. We can't even look at anything to see what's going on because, without the keyboard working, we can't enter the password to get onto the computer... and once the keyboard is working, well, it's working, so there's no way to see what the problem is because at that moment there isn't a problem.