Yes there are Call of Duty games that have co-op.
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Call of Duty 3: Roads to Victory.
Call Of Duty 4: Modern Warfare SAS: Secure Tommorow
No there are not zombies of any kind in any of the modern warfare series of games. There will not be zombies but there will be alien terrorists.
your game might be broken go to any video store and ask if they fix games
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