The helicopter collided with the side of a mountain during a turn after departing from a hospital helipad while on an emergency medical flight to pick up a medical team to care for a critically ill child. The pilot was notified at 0510 by his dispatcher. After checking weather, the pilot called back and said if they want to try it there would be no guarantee. The dispatcher relayed that they (medical center) indicated a great need to go. Prior to departing, the pilot was heard to say 'I feel really uncomfortable about this flight.' The witness stated the pilot had been rotating (rotors) outside a long time and would lift off the pad and then set it back down. From 0700 on 5/7 to 0545 on 5/11, the pilot was either on duty with the National Guard, hospital, flying, or going to school for a total of about 74 hours during a period of about 95 hours. His average rest during this period would have been about 5 hours. The altimeter setting given to the pilot by approach control was 29.69. The pilot's altimeter was found set at 29.80, which would cause the aircraft to be 100 feet lower than indicated.