THE PILOT OF A PA-34-200 ATTEMPTED TO MAKE A SINGLE ENGINE GO-AROUND AND COLLIDED WITH THE TERRAIN NEAR LAKE ELSINORE, CA. THE CFI STATED THAT HE HAD SHUTDOWN THE LEFT ENGINE AND FEATHERED THE PROPELLER TO DEMONSTRATE, TO THE STUDENT, SINGLE- ENGINE PROCEDURES AND PERFORMANCE. THE CFI THEN TOLD HIS STUDENT TO PERFORM A SINGLE-ENGINE LANDING. THE STUDENT WAS HIGH AND FAST ON FINAL. THE STUDENT ATTEMPTED A GO-AROUND BUT, THE ACFT DID NOT RESPOND WITH A POSITIVE RATE OF CLIMB. THE CFI TOOK CONTROL OF THE ACFT BUT, WAS ALSO UNSUCCESSFUL IN GAINING A POSITIVE RATE OF CLIMB. THE ACFT WOULD NOT CLEAR POWER LINES THAT WERE LOCATED AT THE END OF THE RUNWAY. THE CFI DESCENDED THE ACFT AND FLEW UNDER THEM. THE ACFT THEN ENTERED INTO A POSITIVE RATE OF CLIMB BUT NOT ENOUGH TO CLEAR HOUSES IN THEIR FLIGHT PATH. THE CFI ELECTED TO LAND STRAIGHT AHEAD. THERE WERE NO REPORTED MECHANICAL FAILURES OR MALFUNCTIONS WITH THE ACFT PRIOR TO THE ACCIDENT.