FLC OF AN LTT TAXIING IN FOG CONDITIONS BECOMES DISORIENTED AND ENTERS RWY NOT SHOWN ON ARPT DIAGRAM. CONTACT WITH GND HELPS TO REORIENT THEM.

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I RECEIVED CLRNC FROM GND CTL FOR TAXI TO RWY 35. NO SPECIFIC ROUTING INSTRUCTIONS WERE ISSUED. AFTER DEPARTING THE GATE; WE PROCEEDED NE ON TXWY B TO TXWY F. APCHING THE INTXN OF TXWY F; RWYS 6/24 AND 17/35; CAPT STOPPED THE ACFT AND ASKED ME TO ASK FOR CONFIRMATION OF CLRNC ALL THE WAY TO RWY 35. WHILE I WAS TALKING TO GND; AN ACR B737 PASSED IN FRONT OF US DEPARTING ON RWY 35. GND CONFIRMED WE WERE CLRED ALL THE WAY TO RWY 35. WE PROCEEDED ON TXWY F EBOUND ON WHAT BECAME CLOSED RWY 9/27 (NON-DEPICTED ON THE CHART). WE CROSSED RWY 6/24 AND NOTICED THE YELLOW X'S ON RWY 9/27; STOPPED ABEAM THE CTL TWR. GND HAD NOT SEEN US PRIOR TO THIS POINT AND WE CALLED FOR FURTHER CLARIFICATION. GND ASKED FOR OUR POS; WE TOLD THEM THAT WE WERE ON RWY 9/27 AND THAT THE TWR WAS AT OUR 2 O'CLOCK POS. THE GND CTLR RPTED US IN SIGHT AND TOLD US TO MAKE A 180 DEG AND HOLD OUR POS FOR LNDG ACFT. WE COMPLIED. WHILE WAITING CAPT REMARKED; 'SOMEBODY'S GOING TO LAND IN THIS?' NO LNDG TFC APPEARED THEN GND CLRED US TO CROSS THE ACTIVE AND TO PROCEED TO RWY 35 VIA L ON TXWY A AND TO RPT ESTABLISHED ON TXWY A. I RPTED ESTABLISHED AND ASKED FOR CONFIRMATION FOR CLRNC TO CROSS RWY 6/24. GND SAID TO RPT XING RWY 6/24. I COMPLIED. GND CTL THEN INSTRUCTED CAPT TO PHONE THE TWR SUPVR IN RALEIGH UPON OUR ARR. THE REMAINDER OF THE DEP EVOLUTION WAS UNEVENTFUL. THE RWY LIGHTS FOR RWY 6/24 WERE NOT VISIBLE UNTIL AFTER OUR 180 DEG TURN; WHEN GND ANNOUNCED THEY HAD TURNED THEM UP FOR US. LASTLY; IMMEDIATELY AFTER LIFTOFF; TWR ANNOUNCED NEW ATIS OF VISIBILITY DROP TO 1/2 SM. CONTRIBUTING FACTORS: FOG; NO TXWY STRIPE VISIBLE ON TXWYS B; F; A. CLOSED RWY 9/27 NOT DEPICTED ON ARPT DIAGRAM. NO YELLOW X'S VISIBLE ON RWY 9/27 W OF INTXN WITH OTHER RWYS. NOT KNOWING THAT GND CTL DID NOT HAVE US IN SIGHT. THERE WAS ONLY A SINGLE TXWY SIGN FOR TXWYS A; B; F; LOCATED ON THE SIDE OF THE INTXN OPPOSITE OUR DIRECTION OF TURN AND MOTION. LACK OF DETAILED TAXI INSTRUCTIONS (POSITIVE CTL ON GND WOULD HAVE BEEN HELPFUL. DISTR CAUSED BY ACR DEPARTING FLT (UNEXPECTED).