A PLT (WHOSE INSTRUMENT CURRENCY COULD NOT BE DTRMD) TOOK OFF AT NGT IN IMC. SHORTLY AFTER TAKEOFF, THE ACFT CRASHED ABT 1.5 MI FM THE DEP END OF THE RWY. THERE WAS EVIDENCE THAT IT IMPACTED IN AN 85 DEG RGT BANK, NOSE DWN ATTITUDE AT HI SPEED. NO PREIMPACT PART FAILURE WAS FND DRG THE INVESTIGATION; HOWEVER, DRG A PRE-PURCHASE INSPN ON 10/16/90, SVRL DISCREPANCIES WERE NOTED. THESE INCLUDED AN INOP FLT DRCTR, AN AUTOPLT MALFUNCTION & A MISRIGGED FLT CTL SYS THAT ALLOWED THE CTRL WHEEL TO INDC A LEFT TURN WHEN THE ACFT WAS IN LVL FLT. THERE WAS NO RECORD OF THESE BEING REPAIRED. RECORDS SHOWED THE PITOT-STATIC SYS WAS LAST TESTED ON 3/24/88. THE PLT WAS TAKING SINE-AID & TYLENOL FOR A CHRONIC SINUS INFECTION. ALTHOUGH TOX CHECKS INDCD THE PRESENCE OF 50.7 UG/ML OF PSEUDOEPHEDRINE & 36.4 UG/ML OF ACETAMINOPHEN IN THE PLT'S URINE, NONE WAS FOUND IN HIS BLOOD. THE SINUS COND COULD HAVE AFFECTED THE PLT'S BALANCE & EQUILIBRIUM.