C500 AT YIP DEPARTED ON WRONG RWY.

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WE CALLED GND FOR CLRNC. RECEIVED CLRNC TO TAXI VIA RWY 27 FOR TKOF ON RWY 23L. WE WERE PARKED ON THE E SIDE OF THE AIRFIELD. WHEN WE BEGAN TAXI; WE NOTICED THE CAPT'S RMI WAS 180N DEGS OUT FROM THE MAGNETIC COMPASS AND COPLT'S RMI; LOOKING AT THE AIRFIELD DIAGRAM IT APPEARED WE WERE ON RWY 27; TAXIING N FOR TKOF. WE HAD NEVER BEEN INTO WILLOW RUN ARPT AND LOOKING AT THE COMMERCIAL CHART'S DEPICTION OF THE AIRFIELD; IT APPEARED THAT RWY 27 RAN JUST OFF THE E PARKING AREA. AS WE TAXIED ON WHAT WE THOUGHT WAS RWY 27; WE REQUESTED TO HOLD SHORT OF THE ACTIVE TO MANUALLY SLAVE THE CAPT'S RMI TO THE CORRECT HDG. JUST AS THE HDG WAS LINING UP; AND THE COMPASS FLAG WENT AWRY; WE WERE CLRED FOR TKOF. WE PULLED ONTO THE RWY WHICH WE THOUGHT WAS RWY 23. THE MAGNETIC COMPASS WAS STILL SWINGING AND APPEARED TO BE RWY 23. AS WE TOOK OFF; THE COPLT NOTED THAT THERE WAS STILL A DIFFERENCE IN HDGS AND WE WERE NOW SHOWING A HDG OF 270 DEGS INSTEAD OF RWY HDG OF 230 DEGS. I THEN LOOKED OVER AT THE RWY DIAGRAM AND TOLD THE COPLT TO TAKE A SECOND LOOK; THAT I THOUGHT OUR HDG WAS CORRECT; AND WE HAD TAKEN OFF ON RWY 27. AFTER HE TOOK A SECOND LOOK; HE AGREED. WE BOTH FELT PRETTY FOOLISH. WE REVIEWED THE SEQUENCE OF EVENTS ON THE WAY BACK TO DALLAS AND AGREED THAT THE AIRFIELD DIAGRAM AND OUR LOSS OF RMI ALIGNMENT AND MANUAL ALIGNMENT TO TKOF IN A TIMELY MANNER LED TO A SNOWBALL EFFECT. IF WE HAD PULLED ONTO THE RWY; CAME TO A COMPLETE STOP; CHKED ALL HDG INSTS; WE WOULD HAVE SEEN OUR ERROR. ENCLOSED IS A DIAGRAM. YOU CAN SEE THAT IF YOU DO A QUICK SCAN OF THE ARPT; THE RWY 27 PLACEMENT IS ON THE WRONG RWY OR AT LEAST DEPICTS THE WRONG WAY. ANOTHER VISUAL PROB AS WE TURNED ONTO RWY 27; WE SAW A RWY 23 SIGN ABOUT 1000 FT AHEAD -- AGAIN GIVEN THE IMPRESSION THAT IT WAS RWY 23 AND NOT RWY 27.