A C560 CREW; TAXIING FOR TKOF AT PWK; TAXIED ONTO THE DEP RWY.

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WE WERE CLRED TO TAXI FROM PARKING AT PWK OUT FOR RWY 16 VIA TXWY L. WE BOTH LOOKED AT THE ARPT DIAGRAM AND AGREED THAT WE HAD TO TAXI OUT ON TXWY P AND TAKE THE FIRST L WHICH WOULD BE TXWY L. I THEN WENT 'INSIDE' THE ACFT COMMENCING THE TAXI CHKS. SHORTLY AFTER; I FELT THE ACFT TURN SHARPLY TO THE L. I HEARD THE CAPT SAY SOMETHING AND I LOOKED OUTSIDE AND NOTICED THAT WE WERE ENTERING RWY 16/34; THE ACTIVE. THE CAPT CONTINUED THE L 180 DEG TURN AND TAXIED OFF THE RWY AND BACK ON TXWY P. THERE WAS AN ACFT ON FINAL THAT DECIDED TO GO AROUND. I BELIEVED THAT PLANE WAS ANOTHER BIZJET. AT THE TIME OF THIS INCURSION; THERE WAS CONSTRUCTION WORK IN PROGRESS AT THE ARPT. WHEN WE LANDED 40-45 MINS EARLIER WE ADVISED; ON REQUEST; WHICH TXWY WE WERE TAXIING OFF ON; AS THE CTLR WASN'T SURE. HE THOUGHT IT WAS TXWY L; BUT WE NEVER SAW ANY SIGNS FOR TXWY L; WHICH WE ADVISED HIM OF. IT WAS TXWY P; AS PER THE ARPT CHART. BEFORE TAXIING OUT FOR DEP; WE LOOKED DOWN TXWY P AND AGREED THAT THE NEXT PIECE OF XING PAVED AREA MUST BE TXWY L; AS PER THE CHART. HOWEVER; IT IS ACTUALLY RWY 16/34. AS IT TURNS OUT; TXWY L DOES NO LONGER EXIST. IT'S ALL DUG UP; JUST DIRT. THERE IS A HOLD SIGN FOR RWY 16/34 ON TXWY P; BUT BEING INSIDE DOING TAXI CHKS; I NEVER NOTICED. WE WERE EVENTUALLY CLRED TO TAXI ACROSS RWY 16/34 AND VIA TXWY K TO RWY 16; THE ONLY WAY TO GET THERE. CAUSES: I THINK THE FACT THAT THE ARPT DIAGRAM DIDN'T MATCH WITH THE ONGOING CONSTRUCTION WORK CONFUSED US (THE PLTS) AS WELL AS THE CTLRS. WE WERE CLRED TO TAXI ONTO A NON EXISTING TXWY. WE NEVER NOTICED THE RWY HOLD LINE/SIGNAL FOR RWY 16; HAVING OUR MINDS SET ON IT BEING TXWY L WITH A MISSING SIGN. ATC NEVER NOTICED US ENTERING THE RWY; NOT UNTIL THE CAPT TOLD THEM HE WAS ON IT AND TURNING AROUND. I THINK VIGILANCE APPLIES FOR PLTS AND CTLRS -- AND IS IMPERATIVE UNDER THESE CONDITIONS WHERE THE MAP DOESN'T MATCH THE TERRAIN!