Strange noise coming from monitor?

My LCD monitor has been making a loud buzzing/whirring noise whenever I connect it via DVI to my new graphics card (PowerColor PCS+ R7 370). It only makes this noise whenever I get into a game (such as CS:GO or DayZ, the only two games I've tried this with so far). However, when I connect my DVI cable to my motherboard instead of the graphics card, my monitor doesn't make the noise anymore. Nor has my monitor ever made a noise when I had it hooked via VGA to my motherboard. I'm not sure what the issue is here, I've tried these scenarios with two separate monitors as well, same results. Not sure if the problem is both of the monitors, the DVI cable, the graphics card itself, or maybe some sort of sound interference/issue. I hope it isn't the graphics card, as I'm not sure if I can return it at this point. I might add that whenever I have the DVI cable hooked to the graphics card and start a game and it starts the whirring noise, I swear I smell a slight burning scent, but I might just be paranoid because no one else smelled it. Whenever I tab out of the game the whirring stops completely, but it resumes when I pull the game back up. Any help is appreciated!

Edit: Forgot to add the noise happens even when I have my headset with normal game sounds coming through it. Sound seems to come from the monitor itself, as I do not hear the noise when I listen next to my tower.
 
Many possibilities and no easy single answer, so you will have to try different solutions until you find one for yourself. You might want to read through the following articles and plan you approach - easy/cheap ones first, then move on into more expense (buy new cable, etc) and end with the destructive ones (cut this wire or that one).

http://www.tomsguide.com/forum/61686-6-buzzing-noise-speakers-playing-games
http://www.tomsguide.com/answers/id-1778068/buzzing-humming-screeching-sounds-playing-games.html
http://www.tomshardware.com/answers/id-2374004/buzzing-noise-computer-monitor.html
http://www.tomshardware.com/answers/id-2055996/speaker-noise-monitor-playing-games.html

I used Google to find "monitor noise during game play". Other searches may produce better results.
 
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