THE PLT & 2 OBSERVER/TRAINEES WERE ON A FLT ALONG THE LAKE MICHIGAN SHORELINE. AFTER APRX 23 MIN OF FLT, WHILE APCHG TO LAND AT CHICAGO, THE PLT RPRTD AN ENG PROBLEM OF UNKNOWN ORIGIN. HE ATTEMPTED TO LAND IN A PARKING LOT AT A WATER FILTRATION PLANT. AFTER CLRG THE ROOF OF A BLDG, THE ACFT TURNED & SUBSEQUENTLY COLLIDED WITH A RETAINING WALL AT THE EDGE OF THE PARKING LOT. BOTH OBSERVER/TRAINEES WERE FATALLY INJURED. THE PLT WAS SERIOUSLY INJURED & WAS UNABLE TO RECALL THE EVENTS OF THE FLT. THE FUEL SELECTOR WAS FOUND POSITIONED TO THE LEFT FUEL TANK, WHICH REMAINED INTACT. LESS THAN 1 GAL OF FUEL WAS ESTIMATED TO BE REMAINING IN THE LEFT TANK. THE ACFT FUEL TANKS HAD A TOTAL CAPACITY OF 50 GAL, OF WHICH, 13.5 PINTS OF FUEL WAS CONSIDERED TO BE UNUSABLE (LESS THAN 1 GAL PER TANK). APRX 3 HRS AFTER THE ACDNT, NO ODOR OF FUEL WAS NOTED BENEATH THE RUPTURED RGT FUEL TANK. NO WITNESSES OR RECORDS WERE FOUND TO INDICATE THE ACFT HAD BEEN REFUELED BEFORE THE FLT.