A DC9-30 HAS A RWY INCURSION AT MDW; IL; DUE TO SIGNAGE AND FATIGUE.

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I WAS TAXIING FLT; A DC9-30; FOR TKOF TO RWY 31C AT CHICAGO MIDWAY ARPT. WE WERE INSTRUCTED TO TAXI TO RWY 31C VIA TXWYS P AND G. REFERRING TO THE ARPT DIAGRAM; I KNEW I HAD TO CROSS RWY 31R THEN TURN ON TXWY G FOR RWY 31C. TAXIING OUT; I WAS LOOKING FOR RWY 31R AS A REF AND CLUE TO TURN AT THE NEXT INTXN. IT WAS DARK; OVCST; AND THE RAMP AND TXWY WAS WET ASPHALT MAKING IT VERY DIFFICULT TO SEE THE TXWY. ABOUT THIS TIME I CAME UPON A RWY AND JUST ABOUT STOPPED THE ACFT AND ASKED THE FO WHERE'S THE TXWY; SINCE HE HAD BEEN THERE 2 DAYS EARLIER AND I HAD ONLY BEEN THERE ABOUT 6 TIMES OVER THE YRS; HE SAID; 'STRAIGHT AHEAD.' UPON LOOKING TO MY L; I NOTICED AN AIRPLANE ON FINAL AND THOUGHT HE WAS LINED UP ON RWY 31R; THE RWY I WAS LOOKING FOR. BUT RWY 31R WAS UNLIGHTED; I LATER REALIZED; AND WAS AT RWY 31C INSTEAD. MY NOSE WAS OVER THE EDGE LINE AND ADDED PWR TO CLR THE RWY. AT THIS TIME THE ACFT ON FINAL WENT AROUND. I NEVER DID SEE TXWY G AND COMPLETELY MISSED THE SIGN BECAUSE I MISSED SEEING RWY 31R WHICH WAS UNLIGHTED. FURTHER ADDING TO THINGS; GND CTL WAS GIVING A CLRNC AND; THAT AND THE READBACK PREVENTED GND FROM TELLING US TO STOP. DARK; OVCST; WET NIGHT AT AN UNFAMILIAR ARPT WAS A RECIPE FOR TAXI ERRORS. THEY NEED THE AMBER HOLD SHORT TXWY LIGHTS. IF GND WAS RESTR FOR GND ONLY AND CLRNC DELIVERY WAS BEING USED; THEY COULD HAVE TOLD ME I MISSED TXWY G. STILL; IT WAS MY RESPONSIBILITY BUT I BECAME CONFUSED AS TO MY WHEREABOUTS UNTIL THE FO SAID; 'GO THAT WAY;' WHICH RESOLVED THE CONFUSION OR SO I THOUGHT; ONLY TO TAXI ONTO THE ACTIVE. SUPPLEMENTAL INFO FROM ACN 391810: SOMEHOW WE DID NOT SEE RWY 31R THRESHOLD BECAUSE WE WERE TRYING TO NOT MAKE A WRONG TURN AT TXWY Y. THE TXWY SIGNS ARE DIFFICULT TO SEE AT THE END OF CONCOURSE B; BECAUSE OF ACFT PARKED AT THE END OF CONCOURSE B AND ALSO WE WERE TOLD THAT AN ACFT AT THE INTXN OF RWYS 4R AND 31R WOULD GIVE WAY TO US. WITH ITS LNDG LIGHTS ON; IT DISTRACTS AND BLINDS US FROM WHERE WE ARE AND WE WANT TO MAKE SURE WE DON'T COLLIDE. I WAS VERY BUSY WITH THE CHKLIST AND THE DISTRACTIONS OF A COMPACT ARPT; TWO CLOSE ACFT ON THE GND; DARKNESS AT XX15; LAST LEG OF A LONG 4 DAY TRIP; AND A NEW TO THE L SEAT AFTER 14 YRS IN R SEAT CAPT. AS I SAID EARLIER; THE SIGNS AT THIS POINT OF THE ARPT ARE SPACED WIDE APART AND DIFFICULT TO FOLLOW. WITH THE NOSE OF ACFT JUST PAST THE HOLD SHORT LINE OF WHAT WE TOOK TO BE RWY 31R; WAS ACTUALLY RWY 31C; THE LIGHTS OF A LNDG ACFT CAUGHT THE CAPT'S ATTN FIRST; THEN SHORTLY THEREAFTER I SAW THEM. THINKING THEY MUST BE LNDG ON THE WRONG RWY; THE CAPT; HALF-STUNNED; COULD NOT BELIEVE WHAT HE WAS SEEING AND ALL I REMEMBER SAYING AS THEY WERE GOING AROUND AT ABOUT 150 FT WAS 'GO;' AS HE WAS SHOCKED AND CONFUSED SLOWLY ADVANCING THE THROTTLES THEN PUSHING THEM UP RAPIDLY. I WOULD LIKE TO SEE HOLD BARS AT TXWY P AND RWY 31C INTXN.