THE STUDENT WAS A RATED PILOT ON HIS FIRST INSTRUCTIONAL FLIGHT IN THIS AIRCRAFT. AFTER A PRACTICE ABORTED TAKEOFF, THE STUDENT APPLIED POWER TO START ANOTHER TAKEOFF. AT ABOUT THIS TIME, THE AIRCRAFT VEERED TO THE RIGHT. THE INSTRUCTORAPPLIED LEFT RUDDER AND CALLED FOR THE STUDENT TO CUT THE POWER; HOWEVER THE AIRCRAFT CONTINUED TO THE RIGHT AND STRUCK A SNOWBANK. DURING AN INVESTIGATION, THE RIGHT ENGINE WAS OPERATIONALLY CHECKED. WITH THE FUEL BOOST PUMPS OFF, IT FUNCTIONED NORMALLY. HOWEVER, WITH THE BOOST PUMP SWITCH IN THE HIGH POSITION, THE ENGINE WOULD NOT RESPOND PROPERLY WHEN THE THROTTLE WAS RETARDED FROM A HIGH POWER SETTING AND THEN RE-ADVANCED. THE FUEL FLOW REMAINED HIGH AND BLACK EMISSIONS CAME FROM THE EXHAUST SYSTEM. WHEN THE THROTTLE WAS RETARDED, THE ENGINE WOULD STOP RUNNING. THE LEFT ENGINE OPERATED NORMALLY DURING THE SAME CHECK. THE INSTRUCTOR SUSPECTED A MALFUNCTION OF THE FUEL PUMP PRESSURE SWITCH.