I didn't make it!
I just got the Game of the Year edition and everything installed fine and the multiplayer works. However, when I try to start single player, the Call of Duty logo appears and remains for 1-2 minutes. After that it says CodSP.exe has encountered a problem and needs to close. Reinstalling doesn't fix it. My friend also had the GotY version and it works fine one his system, but when I tried my copy on his computer I got the same problem.
It sounds like something wrong with your copy, take it back to the shop you got it from and tell them that you have a defective game