how new/old is your pc? Is it under warranty? If it is, get a certified technician to open the case so you don't void warranty. A Comptia A+ certification usually is acceptable, though some manufacturers want the tech to have a cert from the manufacturer.
Now if it is not under warranty, power down, unplug the unit, crack open, um sorry, just open the case and look inside. Chances are there'll be a lot of dust and even dust balls. Get a can of compressed air and blow these out, focusing especially on the fans, and the heat sink over your processor. With the case open, plug up the computer again and try to duplicate the problem. You should be able to pinpoint what part of the computer is making the noise.
From what little you've provided so far, I suspect we're going to be looking at your video card, if you have one, and not just the motherboard. If there is dust, the unit might be ramping up the fans to deal with the excess heat caused by both dust and the added demands of the game.
More details about the system and what you see/hear will help. A snapshot of the pc interiors with the location of the sound origin circled might not hurt either.