ACR FREIGHTER CREW MISSES TAXI TURN AND EXPERIENCES RWY INCURSION. NO TFC CONFLICT OCCURS.

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AFTER BEING CLRED TO RWY 07 AT ROCKFORD; IL (RFD); WE EXITED THE RAMP AREA AT THE THROAT OF 'F-1.' WE CONTINUED TO TAXI STRAIGHT AHEAD ONTO 'G' TXWY MISSING THE R TURN ONTO TXWY 'F.' AFTER A VERY SHORT DISTANCE ON 'G' TXWY WE STARTED A R TURN ONTO RWY 07/25 THINKING IT WAS TXWY 'F' WHICH WAS THE PLANNED ROUTE TO RWY 07/25. TXWY 'F' IS THE PARALLEL TXWY TO RWYS 07/25. JUST AFTER MAKING THE TURN ONTO RWY 07/25 I REALIZED THE MISTAKE AND AT THE SAME TIME WAS NOTIFIED BY GND CTL THAT WE TAXIED ONTO THE RWY. WE ASKED AND WAS THEN CLRED TO EXIT THE RWY AT TXWY 'K' AGAIN ONTO TXWY 'F.' WE CONTINUED FOR TAKEOFF ONTO RWY 07 PER OUR TAXI AND TAKEOFF CLRNC. WEATHER CONDITIONS WERE VMC AT DAWN; WITH A LIGHT MIST AND STANDING WATER ON THE RAMP AND TXWYS FROM HEAVY RAIN AND THUNDERSTORM ACTIVITY SHORTLY BEFORE BLOCKOUT. TXWY LIGHTS WERE NO LONGER ILLUMINATED DUE TO BEGINNING DAYLIGHT CONDITIONS. THE RAMP AND TAXIWAY MARKINGS WERE PARTIALLY OBSCURED SOMEWHAT BECAUSE OF STANDING WATER AND SUBSEQUENT GLARE FROM RAMP LIGHTS. POSSIBLE CONTRIBUTING FACTORS INCLUDE: FATIGUE -- WE WERE ALREADY ON DUTY OVER 9 HRS AND MISSED OUR USUAL NAP IN ROCKFORD BECAUSE OF A LONG WEATHER DELAY LEAVING OUR DEP ARPT (JFK) THE NIGHT BEFORE. WE ALSO DELAYED DEP FROM (RFD) DUE TO AN ACFT MECHANICAL. ADDITIONALLY WEATHER CONDITIONS AT ROCKFORD PARTIALLY OBSCURED BOTH RAMP AND TXWY MARKINGS ALLOWING THE RAMP AREA TO APPEAR AS PART OF TXWY 'G;' THUS MISSING THE IMMEDIATE R TURN ONTO TXWY 'F.' WE MAY HAVE BEEN COMPLACEMENT BECAUSE ROCKFORD IS A VERY FAMILIAR ARPT. PAINTED TXWY AND RAMP MARKINGS SHOULD NOT BE ALLOWED TO DULL OR WEAR SO MUCH THAT STANDING WATER AND GLARE MAKE THEM DIFFICULT TO SEE. TXWY LIGHTING SHOULD CONTINUE TO BE ILLUMINATED UNTIL WELL AFTER DAWN. ROCKFORD HAS ONLY TXWY EDGE LIGHTING. TXWY CENTER LINE LIGHTING WOULD HAVE BEEN A GREAT HELP. NOTE: NO OTHER ACFT WERE IN THE AREA WHEN THIS OCCURRED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR EMPHASIZED THAT EARLY DAWN LIGHTING; TXWY LINE CONTAMINATION BY STANDING WATER; AND THE TXWY LIGHTS BEING TURNED OFF EARLY CONTRIBUTED TO THIS RWY INCURSION. HE ALSO NOTED THAT FATIGUE CONTRIBUTED TO A LESSENING OF AWARENESS AND COCKPIT COORDINATION.