WHEN THE CAR WAS 2 WEEKS OLD, WE RETURNED FROM A DRIVE AND FOUND THE CAR WOULD NOT SHUT OFF, EVEN WITH THE IGNITION IN THE "OFF" POSITION AND THE KEY REMOVED. THE ENGINE SOUNDED AS THOUGH IT WAS TRYING TO START ITSELF, EVEN THOUGH IT WAS STILL RUNNING. I PUT THE KEY BACK IN AND TURNED IT TO THE "ON" POSITION, AT WHICH POINT THE UNUSUAL NOISE DISAPPEARED, AND THE CAR SEEMED TO IDLE NORMALLY. I TURNED IT OFF AGAIN, AND THE NOISE RETURNED AS THE CAR KEPT RUNNING. I TURNED THE KEY ON AND OFF A FEW TIMES BEFORE THE ENGINE FINALLY STOPPED. AS I GOT OUT OF THE CAR, I NOTICED SMOKE RISING FROM UNDER THE HOOD. I OPENED THE HOOD AND SAW THAT A FIRE WAS BURNING ON THE STARTER AND THE NEARBY RUBBER HOSES. I UNSUCCESSFULLY TRIED TO BLOW OUT THE FLAMES, WHICH WE PUT OUT USING A FIRE EXTINGUISHER FROM OUR APARTMENT BUILDING, WHICH WE WERE PARKED IN FRONT OF. ALL DAMAGED PARTS WERE REPLACED BY THE DEALERSHIP SERVICE DEPARTMENT, ALTHOUGH THERE IS STILL A BURNT SMELL EVIDENT AFTER DRIVING THE CAR. I INFORMED HONDA OF THE PROBLEM THROUGH THEIR "NEW OWNER SURVEY" AND A LETTER TO THEIR CUSTOMER RELATIONS ZONE OFFICE. *AK