A BEECH 1900 FLC LOST COM ENRTE TO OFK.

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WE DEPARTED LBF FOR OFK. OUR CLRNC WAS LBF DIRECT OBH DIRECT OFK AND OUR ALT WAS FL250. WE TOOK OFF RWY 30. OUT OF 4500 FT MSL WE CALLED DEPARTING THE AREA E. WE MADE OUR INITIAL CONTACT WITH ATC AT 6000 FT MSL. I CAN'T REMEMBER THE RESPONSE FROM ATC OR IF THERE WAS ONE. OUT OF 10000 FT MSL WE CALLED OUR COMPANY BACK TO LET THEM KNOW OUR TIMES IN AND OUT. WE HEADED ON COURSE AND OUT OF FL220. WE REQUESTED FL230 AS A FINAL INSTEAD OF FL250. THIS IS WHEN ATC ASKED WHERE WE WERE. APPARENTLY OUR XPONDER #1 WAS MALFUNCTIONING. SO WE RECYCLED TO #2. IT WASN'T UNTIL 10 MINS AFTER DEPARTING AND AT FL230 (40-45 MI E OF LBF) WERE WE IN RADAR CONTACT. POSSIBLE CAUSES: CREW WAS RUNNING 1 1/2 HRS LATE AND IT WAS XA30 (FATIGUED). LATE AT NIGHT THE CTLR WAS WORKING A LARGE AREA AND WAS VERY BUSY. INACTIONS: CREW NOT REALIZING WE WERE NOT GIVEN 'RADAR CONTACT.' ALSO; WE DIDN'T REALIZE OUR XPONDER WASN'T SHOWING ANY INTERROGATION. ALSO; IT HAD BEEN AT LEAST 10 MINS FROM RECEIVING OUR CLRNC AND OUR VOID TIME WAS 10 MINS. THE CTLR DIDN'T QUERY US ON OUR LOCATION. SHORTLY AFTER BEING FOUND ON 'RADAR CONTACT' WE WERE SENT TO THE NEXT CTLR. HE HAD TIME SO WE QUESTIONED HIM ON HOW WELL OUR XPONDERS WERE WORKING. AT THAT TIME THEY SEEMED TO BE WORKING FINE. THE ONLY THING I CAN THINK OF TO STOP THIS FROM HAPPENING AGAIN IS NOT BEING CLRED ALL THE WAY UP TO OUR FINAL ALT. THIS WAY WE WOULD HAVE TO MAKE SURE WE HAD 'RADAR CONTACT ASAP.' ALSO; THE CREW SHOULD MAKE SURE TO TALK TO ATC.