THE ACFT ENTERED AN UNCOMMANDED DIVE AT ABOUT 11,000 FT MSL, WITH RECOVERY MADE BELOW 2,000 FT MSL. INVESTIGATION REVEALED THAT DURING THE DESCENT, IN ORDER TO ACCOMODATE OTHER AIR TRAFFIC, THE PLT EXCEEDED VNE SPEEDS. SHORTLY, THEREAFTER THE ELEVATOR TRIM SYSTEM MALFUNCTIONED & JAMMED THE TRIM IN THE FULL NOSE DOWN TRIM POSITION. WHEN A BRIEF FLARE-UP OF SMOKE & SPARKS ERUPTED UNDER THE RT INSTRUMENT PANEL ON THE LT SIDE OF THE CONTROL COLUMN THE PLT DELAYED AN EMERGENCY BUT DID NOT RELAY INFORMATION CONCERNING THE CONTROL PROBLEM. POST INCIDENT EXAMINATION FOUND THE ELEVATOR TRIM TAB CABLE BROKEN AT THE TRIM SERVO, LOCATED UNDER THE AFT CABIN FLOOR JUST FORWARD OF THE CABIN ENTRANCE DOOR. FRAYED IN AN IRREGULAR MANNER OVER A NINE INCH AREA, THE LOOSE CABLES BECAME ENTANGLED IN THE ELECTRICAL POWER DIODES LOCATED BENEATH THE CONTROL PEDESTAL. INSPECTION REVEALED THE FRICTION CLUTCH OPERATED AT TOO HIGH TORQUE & THE CABLES WERE OUT OF ALIGNMENT CAUSING HEAT TO OTHER COMPONENTS.