WHILE DEPG ON AN IFR FLT TO VFR CONDS, THE PLT FAILED TO PROVIDE THE CORRECT TRANSPONDER CODE PER ATC CLNC. THE LOCAL CONTROLLER (CTLR) REMINDED HIM TO SET THE CORRECT CODE & THE PLT SUBSEQUENTLY REPLIED 'I'M HAVING A PROBLEM RIGHT NOW . . . I'VE GOT TO GET STRAIGHTENED AWAY . . .' THE CTLR AGAIN REMINDED THE PLT ABT THE CORRECT TRANSPONDER CODE & ADZD OF TRAFFIC AHEAD. SUBSEQUENTLY, THE ACFT BEGAN A SHALLOW DSCNDG LEFT TURN, THEN HIT THE TOPS OF 3 TALL PALM TREES, CRASHED IN AN APT COMPLEX & BURNED. SVRL WITNESSES RPRTD ENG PROBLEMS, BUT NO PREIMPACT PART FAILURE OR MALFUNCTION WAS FND DRG THE INVESTIGATION. ALTHOUGH PROPERLY CERTIFICATED FOR THIS FLT, THE PLT HAD RECENTLY FAILED AN INSTRUMENT FLT TEST. THE FAA WAS IN THE PROCESS OF REVOKING HIS INSTRUMENT PRIVILEGES. THE PLT RPRTDLY WAS EXPERIENCING SERIOUS PERSONAL & FINANCIAL PRBLMS STEMMING FROM HIS WIFE'S ILLNESS & EXTENSIVE HOSPITALIZATION; HIS FLT INSTRUCTOR RPRTD THESE PRBLMS WERE ADVERSELY AFFECTING HIS FLYING SKILLS.