1) Is it possible that you are at the near focus point of your lens? If you are indeed within that range, the lens (at least G versions)will not hunt for focus, and it will not focus. If you are setup not to shoot without focus, the camera will not shoot. That one had me stymied for some time before I figured it out.
2) When your goal is to take a shot even if it won't win a Pulitzer, then what I do is: a- I keep my AE-L/AF-L button set to force the shutter to fire regardless of focus. b- If I know that my buffer is not full, and the shutter won't fire; I depress the AE-L/AF-L button while pressing the shutter release. I've never had that to fail.