A C550 FLT CREW INADVERTENTLY TOOK OFF FROM RWY 23 THAT WAS NOTAMED CLOSED AT SHR.

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ON BOARD WE HAD A COPY OF THE NOTAMS FOR SHR; WHICH INCLUDED THE FACT THAT RWY 5/23 WAS CLOSED. WE LANDED ON RWY 32; TAXIED TO THE FBO; AND DEPLANED OUR PAX. AFTER ENG START AND COMPLETION OF THE PRE-TAXI CHKLIST; THE PF AND MYSELF DISCUSSED GOING TO RWY 23 FOR TKOF; SINCE WIND AND TFC WERE NOT AN ISSUE. ALSO; RWY 23 IS MUCH CLOSER TO THE FBO THAN IS RWY 14/32. WE COMPLETELY FORGOT ABOUT THE NOTAM CLOSURE OF RWY 5/23. AS WE WERE TAXIING OUT; WE ANNOUNCED OUR INTENTIONS TO DEPART ON RWY 23 ON THE CTAF 3 OR 4 TIMES. THERE WAS A C172 TURNING FINAL FOR RWY 14 (WHICH INTERSECTS RWY 5/23) AND WE TOLD HIM THAT WE WOULD WAIT. HE ANNOUNCED CLR OF ALL RWYS; AND WE ANNOUNCED OUR INTENTION TO DEPART ON RWY 23. SHORTLY AFTER GETTING AIRBORNE; WE NOTICED CONES BLOCKING THE W 500 FT (APPROX) AND BEYOND THAT THE 'X.' AT ABOUT THE SAME TIME; AN INDIVIDUAL; WHO WE BELIEVE WAS WORKING WITH SOME CREW AT THE APCH END OF RWY 32; TOLD US THAT WE HAD JUST TAKEN OFF ON A CLOSED RWY. HE ASKED US IF WE HAD CHKED THE NOTAMS. WE TOLD HIM THAT THERE WAS NO 'X' ON THE APCH END OF RWY 23. HE SAID IT WAS IN THE GRASS SO THAT PLANES COULD STILL TAXI THERE. THAT WAS THE END OF OUR DISCUSSION WITH HIM. IN RETROSPECT; WE SHOULD HAVE REMEMBERED WHAT WE HAD DISCUSSED ABOUT 15 MINS EARLIER ABOUT THE CLOSED RWY. WE DIDN'T! BUT ALSO; THE INDIVIDUAL ON THE RADIO SHOULD HAVE HEARD OUR INTENTIONS TO DEPART RWY 23; BUT SAID NOTHING. THE C172 LNDG BEFORE US SAID NOTHING. AND THERE WERE NO SIGNS ON THE DEP END OF THE RWY THAT WE COULD SEE THAT INDICATED THAT THE RWY WAS CLOSED. SUPPLEMENTAL INFO FROM ACN 619535: AFTER THIS INCIDENT AT OUR SAFETY MEETING; WE CONCLUDED THAT WE WERE AT FAULT ALONG WITH THE ARPT MGR FOR NOT LABELING RWY 23 CLOSED WHERE WE COULD RAPIDLY SEE IT. SO NOW WE PAY EXTRA ATTN AND DETAIL TO THE NOTAM AT EACH ARPT WE TRAVEL IN OUR BRIEFING. I THINK THE CONSTRUCTION PERSON'S INTENTION WAS TO LET US KNOW AFTER THE FACT SO THAT WE COULD GET VIOLATED.