COMMUTER ACFT IS IMPROPERLY DEICED BY CONTRACT GND PERSONNEL; TAIL NOT DEICED. MUST DIVERT LAND.

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WE RPTED FOR DUTY IN FYV; AR; AT XA15 AM AFTER A 9 HR 10 MIN OVERNIGHT. DURING THE EARLY MORNING; A STRONG COLD FRONT MOVED THROUGH THE AREA. ON PREFLT; THE ACFT WAS COATED WITH A LIGHT LAYER OF ICE AND SNOW. WE WERE TOLD THAT THE COMPANY DEICER WAS INOP AND THE LCL FBO WOULD BE DEICING THE ACFT. WE LOADED THE PAX AND CARGO AT APPROX XB45. THE DEICER THE FBO WAS USING WAS A LADDER TYPE PULLED BY A TUG. I NOTICED IT WAS SLIGHTLY SMALLER THAN THE COMPANY'S DEICER. THE COMPANY'S RAMP PERSONNEL INFORMED US THAT THE FBO MAY NOT HAVE ENOUGH FLUID TO DEICE THE AIRPLANE. THEY STARTED TO DEICE THE AIRPLANE -- BEGINNING WITH THE TRAILING EDGE OF THE L WING AND WORKING CLOCKWISE AROUND THE ACFT FINISHING WITH THE TAIL. WE RECEIVED A SIGNAL THAT THE DEICING HAD BEEN COMPLETED. WE WERE CLRED TO START THE ENGS FOR TAXI. WE TAXIED TO RWY 34 FOR DEP. I INSTRUCTED THE FO TO DO A 'PRE-TKOF CONTAMINATION CHK.' THIS IS DONE BY OPENING THE REAR CABIN AIR STAIR DOOR AND LOOKING AT THE UPPER SURFACE OF THE WINGS. SINCE IT IS A T-TAIL AIRPLANE; THE UPPER SURFACE OF THE TAIL IS NOT VISIBLE. THE FO RETURNED AND INFORMED ME THAT THE AIRPLANE WAS FREE OF ICE AND SNOW. WHILE HOLDING FOR TKOF; ANOTHER ACFT MADE A MISSED APCH ON THE LOC RWY 16 APCH AND DIVERTED TO THEIR ALTERNATE. WE THEN RECEIVED TKOF CLRNC. THE VISIBILITY AT TKOF WAS 1 MI WITH LIGHT SNOW; WIND FROM 300 DEGS GUSTING TO 28-30 KTS; TEMP 7 DEGS F (ABOUT THE SAME AS DURING DEICING MINS EARLIER). WE SELECTED LEVEL 2 ANTI-ICE ON (ENGS; PROPS; AND HORNS). BEFORE TKOF CHKLIST WAS COMPLETED. IT WAS MY LEG TO FLY AND I BROUGHT THE PWR LEVERS TO 'TKOF PWR.' DURING THE TKOF ROLL; I NOTICED THE NOSE WAS TRYING TO COME OFF THE GND PREMATURELY. THE FO CALLED OUT 'V1; ROTATE.' ON ROTATION; THE ACFT PITCHED UP EXCESSIVELY. I COMPENSATED BY APPLYING FORWARD PRESSURE ON THE YOKE AND 'NOSE DOWN' TRIM. THE FO CALLED 'POSITIVE CLB' AND I COMMANDED 'GEAR UP.' THE ACFT WOULD NOT ACCELERATE PAST 120 KTS AND WAS SLOW TO CLB. AT ACCELERATION HEIGHT; I CALLED FOR THE 'CLB SEQUENCE.' I WAS ABLE TO ACCELERATE TO VM1B0 ICE AND I CALLED FOR FLAPS TO 'ZERO' AND 'AFTER TKOF CHKLIST.' THE ICE DETECTOR CAME ON AND WE SELECTED LEVEL 3 DEICE ON (WING AND TAIL BOOTS). THE ACFT WAS STILL PITCHING UP AND I HAD FULL NOSE-DOWN TRIM. WE DECIDED TO CONTINUE THE CLB ABOVE THE CLOUDS AND OUT OF THE LIGHT RIME ICING CONDITIONS. WE LEVELED AT 17000 FT. IN LEVEL FLT; THE TRIM WAS STILL AT FULL NOSE-DOWN LIMIT AND LIGHT FORWARD PRESSURE WAS REQUIRED TO KEEP THE AIRPLANE LEVEL. OVER SPRINGFIELD; MO; VOR (SGF); I DECIDED NOT TO CONTINUE THE FLT TO STL. WE INFORMED ZKC WE WERE HAVING TROUBLE WITH THE TRIM AND WANTED TO LAND IN SGF. DURING THE DSCNT INTO SGF; WE FLEW THROUGH A TEMP INVERSION AND THE ICE MELTED OFF THE AIRPLANE. THE TRIM GRADUALLY RETURNED TO NORMAL AND WE LANDED IN SGF WITHOUT INCIDENT. IT IS MY BELIEF THAT THE TAIL-PLANE WAS NOT PROPERLY DEICED AND WE STILL HAD ICE AND/OR SNOW ON THE UPPER SURFACE OF THE TAIL; WHICH IS NOT VISIBLE TO THE CREW.