ACFT EQUIP PROB INTERNAL ICING OF THE ELEVATOR TRIM SYS AND ELEVATOR MIXER.

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DEPARTED RDD DURING A HVY RAIN STORM WITH A MIX OF HAIL AND RAIN. THE ACFT HAD BEEN ON THE GND FOR 20 MINS DURING THIS STORM. THE FO WAS FLYING THE ACFT AND WE DISCUSSED OUR OPTIONS CONCERNING THE DEP. WE ELECTED TO FOLLOW THE PRESCRIBED SID; THE HOMELAND 1 DEP; WHICH WOULD TAKE THE FLT ON AN EASTERLY HDG AWAY FROM THE STORM. WHILE WAITING FOR CLRNC TO TKOF; MOST OF THE HAIL STORM HAD TURNED TO RAIN. THERE WAS SOME HAIL ON THE ACFT; BUT MOST THAT COULD BE SEEN HAD WASHED AWAY. ONCE THE FLT HAD BEEN CLRED FOR TKOF; SMALL AMOUNTS THEN REMAINING WERE BLOWN OFF AT ABOUT 20 KTS AIRSPD. THE FLT DEPARTED AND ENCOUNTERED HVY RAIN AND HAIL RIGHT AFTER TKOF. FLT TURNED TO THE EASTERLY HDG AND FLEW OUT OF THE RAIN STORM. THE FO HAD TURNED THE AUTOPLT ON AND WAS COMMANDING THE ACFT THROUGH THE FLT DIRECTOR. THE FLT PASSED THROUGH THE FREEZING LEVEL AT 3000 TO 4000 FT MSL. THE ACFT ANTI-ICE SYS WERE TURNED ON; BUT NO ICE BUILDUP ON THE WINGS OR WINDSHIELD WAS NOTED. AT THIS POINT; THE FLT WAS CLRED DIRECT RBL VOR AND TO MAINTAIN 11000 FT. WE WERE THEN CLRED TO MAINTAIN 12000 FT AND TO EXPECT DIRECT PYE. AT THIS TIME; THE ACFT ON AUTOPLT BEGAN TO LEVEL OFF AT 12000 FT. THE FO NOTED THE WHITE OUT OF TRIM LIGHT ON FLT DIRECTOR PANEL AT WHICH POINT HE TOOK THE ACFT OFF THE AUTOPLT. THE ACFT PITCHED DOWN UNCOMMANDED. THE FO ANNOUNCED 'ELEVATOR TRIM RUNAWAY' AT WHICH TIME WE FOLLOWED THE EMER PROCS FOR ELEVATOR TRIM RUNAWAY. ONCE WE COMPLETED THIS EMER PROC; WE REALIZED THAT THERE WAS SOMETHING ELSE WRONG. WE DECLARED AN EMER AND DIVERTED TO SMF. ENRTE WE BOTH CHKED THE RESPONSE OF THE ELEVATORS. IT FELT LIKE SOMETHING WAS BINDING THE CTLS AND NOT ALLOWING THEM TO WORK IN THEIR NORMAL WAY. WE THEN SLOWED THE ACFT DOWN TO 200 KTS TO SEE IF THERE WAS ANY ABNORMAL OR UNDESIRABLE CTL FORCES NEEDED TO KEEP THE ACFT STRAIGHT AND LEVEL. WE FOLLOWED THE SAME PROC AND LOWERED THE LNDG GEAR. WE CONTINUED DSNDING INTO SMF FOR LNDG. WE LANDED IN SMF AND HAD THE ACFT INSPECTED. IT WAS NOTED BY BOTH FLC MEMBERS AND MAINT THAT THERE WAS A LOT OF WATER DRAINING FROM THE ACFT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR FLIES THE EMB-120. RPTR BELIEVES THAT THERE WAS ICING INTERNAL TO THE ACFT CAUSING THE CTLS TO BE STIFF. THE BAGGAGE DOOR WAS LEFT OPEN DURING ABOUT 20 MINS OF THE STORM ALLOWING WATER INTO THE BELLY OF THE ACFT. THE SURFACE TEMP WAS QUITE WARM; ABOUT 54 DEGS; BUT THE FREEZING LEVEL WAS QUITE LOW; ABOUT 3000 FT; ALLOWING ICE TO FORM ON THE CTL MIXER. THE RPTR HAS HEARD OF OTHER PLTS HAVING SIMILAR PROBS WITH THE SAME ACFT TYPE. ONE OF HIS PAX WROTE BOTH THE ACR AND THE FAA COMPLAINING ABOUT TAKING OFF IN A HAIL STORM. HAIL IS QUITE DISTRACTING TO THOSE INSIDE THE ACFT. THE RPTR HAS NOT HEARD FROM THE FAA ON THIS. HE BELIEVES THAT; IF THE FO HAD BEEN HAND-FLYING THE ACFT; THE PROB WOULD HAVE BEEN NOTICED EARLIER AND MIGHT NEVER HAVE BECOME SO LARGE AS THE CTLS COULD HAVE BEEN WORKED TO PREVENT THE ICE ACCUMULATION.