Try the following, several times if necessary.
Look in the camera with the lens removed, is the mirror in the normal position and not askew or fallen off? (A common problem with older 5D2's especially in humid climates). If the mirror is attached, put the camera in bulb mode and while looking into the lens mount without a lens trigger the shutter and watch and then release the shutter - did everything go OK or was there anything weird with the shutter? If all is OK, go to the next paragraph..
Put a fully charged battery in the camera, turn the camera on and wait for a few seconds. Leaving the camera on, remove the battery, wait for 10 seconds, reinstall the battery. Turn the camera off, then on. Repeat if necessary. If after 4 tries this does not work, it is likely that the shutter mechanism has failed.