SVRL MECHANIC WITNESSES AT THE ARPT SAID THE RGT ENG BACKFIRED & TRAILED BLACK SMOKE DURING THE TAKEOFF GROUND ROLL. RPRTDLY, THE TAKEOFF ROLL WAS ABOUT 80% LONGER THAN NORMAL. WITNESSES SAID THE ACFT STAGGERED OFF THE GROUND, WAS SLOW & NEVER GOT ABOVE 100 FEET AGL. THE PLT RPRTD TO THE TOWER THAT THE FLT HAD TO COME BACK TO THE RWY. SHORTLY THEREAFTER, WITNESSES SAW THE ACFT ENTER A STEEP LEFT TURN, APPARENTLY STALL, THEN CRASH INTO SOME TENNIS COURTS. AN INVESTIGATION REVEALED EVIDENCE THAT THE RGT ENG HAD LOST POWER. A MODIFICATION KIT FOR THE FUEL INJECTOR REFERENCE AIR LINES WAS INCORRECTLY INSTALLED & ALLOWED AN UNFILTERED AIR SOURCE. SPECTRAL ANALYSIS OF RESIDUE (FROM THE RGT ENG TURBO CHARGER COMPRESSOR) REVEALED THAT IT HAD THE SAME COMPOSITION AS THE ALTERNATE AIR DOOR SEAL. TRACES OF THE MATERIAL WERE FOUND IN THE FUEL INJECTOR REFERENCE AIR LINE.