I found out what year MC4 WAS SET!
In the single-player campaign mission Terminus, which takes place in a train station, there are these little black boards that you can find that says the date. It says the date is August 20, 2037. So, based on this information, we can assume Modern Combat 4: Zero Hour was set somewhere in 2037, maybe the beginning was 2036, maybe the ending was in 2038.
In the multiplayer map Fracture, which is based around Terminus, the same black boards say 2037.
Pretty cool, right? Try going to your MC4 and check whether these boards also say August 20, 2037. SHARE THIS WITH EVERYONE ON THIS WIKI YOU KNOW! We never knew when the game was set until now, where we have an approximation.
In-game, be sure to keep you eyes peeled for details like these!