After taking off at NGT on RWY 34L, the ACFT was mnvrd to a left dnwnd (same RWY). According to witnesses, the eng(s) went to a hi pwr setting on dnwnd, but the ACFT speed rmnd slow. Apchg (abeam) midfield, the ACFT turned left, then went into a dscnt & crashed west of the arpt. Impact was on an ESE hdg, in a 15 to 17 deg dscnt. The left fuel slctr was fnd in the 'off' psn, but the actuating cable had pulled thru the housing (presumably drg impact). The rgt fuel slctr was on. Both props sepd fm the crankshaft with evidence of torsional failure. There was a history of elevator trim (E/T) problems. Just bfr this flt, maint had been performed on the E/T. E/T actuators were fnd reversed, which reversed the drctn of trim. Both E/T tabs were fnd byd the full nose dwn trim psn. Calculated force to override at the full nose dwn psn was: 121 to 136 lbs at 100 kts, 197 to 203 lbs at 150 kts, 200 to 305 lbs at 200 kts. Also, E/T chain was fnd off of the sprocket & jammed btn the brg plate & a bracket; 1 of 2 bolts was missing fm brg plate; otr bolt was finger tight.