PROVINCETOWN-BOSTON AIRLINES FLT 1039, AN EMBRAER EMB-110P1, WAS CLEARED TO TAKEOFF ON RWY 31 AT 1812 EST. DRG THE INITIAL CLIMB NR THE DEPARTURE END OF THE RWY, THE CAPT ROUTINELY ACKNOWLEDGED AN INSTRN TO CONTACT DEP CONTROL (CTL). SHORTLY THEREAFTER, THE ACFT ENTERED A STEEP DSCNT & CRASHED IN AN INVERTED, NOSE DWN ATTITUDE, THEN BURNED. AN INVESTI-GATION REVEALED THE ELEVATOR (ELEV) & HORIZONTAL STABILIZER (STAB) HAD SEPARATED IN FLT. THE STAB WAS FND ABOUT 1100 FT FM THE MAIN WRECKAGE. THE ELEV TRIM WAS FND IN A PSN TO TRIM THE ACFT FULL NOSE DWN. THERE WAS EVIDENCE OF A MALFUNCTIONOF THE ELEV CTL SYS OR ELEV TRIM SYS, WHICH RESULTED IN A PITCH CTL PROBLEM; THEN REACTION OF THE FLTCREW TO CORRECT THE PROBLEM OVERSTRESSED THE LEFT ELEV CTL ROD. ALSO, THERE WAS EVIDENCE THAT THIS RESULTED IN AN ASYMMETRICAL ELEV DEFLECTION & OVERSTRESS FAILURE OF THE STAB ATTACHMENT STRUCTURE. HOWEVER, THE SAFETY BOARD WAS UNABLE TO DETERMINE THE PRECISE PROBLEM WITH THE PITCH CTL SYS.