B737 CREW TOOK OFF WITH NO TWR CLRNC. THE CREW THOUGHT THE TWR WAS CLOSED.

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PREFLT CHKS IN PROGRESS; WE PICKED UP IFR CLRNC ON 120.4. CTLR GAVE 'CLRED AS FILED; MAINTAIN 2000 FT.' PREFLT CHKS COMPLETED AND CABIN SECURED FOR PUSH. WE CALLED 120.4 FOR PUSH AND START. NO REPLY. AFTER REPEATED ATTEMPTS WE TRIED (123.7) WITH SAME RESULTS. ATTEMPTS ON COM #2 WERE THE SAME -- NO REPLY. WE KNEW THE RADIO WORKED BECAUSE WE HAD JUST TALKED ON THE COMPANY FREQ. CAPT NOTICED 10-7 PAGE SHOWED NO TWR OPS FROM XA00. WE FIGURE THAT EXPLAINS THE SILENCE FROM GND/TWR CALLS. WE THEN REVERTED TO UNCTLED ARPT PROCS. PUSHBACK WAS ON OUR OWN (FACING THE TWR). WE COULD SE THAT THERE WAS SOMEONE IN THE TWR; BUT FIGURED THEY WERE JUST SETTING UP TO OPEN AT XB00. AFTER STARTING AND DISCONNECTING; CLRING GND CREW AWAY; I CALLED OVER CTAF; 'ACR X TAXIING FROM AIRLINE RAMP TO RWY 14.' ALL NORMAL CHKS COMPLETE AND READY FOR TKOF; I ANNOUNCED OVER CTAF; 'ACR TAKING ACTIVE RWY 14 FOR DEP TO THE W.' NO REPLY WAS EVER HEARD FROM AN ATC FACILITY OR ANY OTHER TFC IN AREA. CAPT PERFORMED NORMAL TKOF. PASSING ABOUT 1200 FT MSL WE TRIED ONE MORE CALL ON 123.7 BEFORE CALLING ZHU ON 127.65. THIS TIME; CTLR ANSWERED AND INFORMED US WE TOOK OFF WITHOUT A CLRNC. WE EXPLAINED REASONS FOR OUR ACTIONS; NO REPLY FROM CTLR; AND LEFT IT AT THAT.