AN ACR PLT RPTS TAXIING ONTO RWY 4/22 AT TXWY C AFTER MISSING TXWY P BECAUSE OF A WET SURFACE AND NO HOLD SHORT LIGHTS BEFORE RWY 4/22 ENTRY.

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DURING OUR TAXI TO RWY 15R AT BWI WE WERE INSTRUCTED BY GND TO TAXI VIA TXWY C AND P TO RWY 15R. IT WAS RAINING SLIGHTLY AT DAWN MAKING THE PAVEMENT GLOSSY AND MARKINGS DIFFICULT TO SEE. OUR ACFT WAS LINED UP WITH TXWY C SO WE TAXIED STRAIGHT TO P AND ENDED UP ON RWY 4/22; WHICH WAS INACTIVE; AT THE TIME WE IMMEDIATELY RECOGNIZED THE MISTAKE AND NOTIFIED GND. GND INSTRUCTED US TO TAXI VIA TXWY P1 AND TXWY P TO RWY 15R WHICH WAS COMPLIED WITH AND THERE WAS NO FURTHER INCIDENT. THERE ARE NO HOLD SHORT LIGHTS OR BARS AT THE INTXN OF TXWY C OR RWY 4/22. WITH THE GLOSSY PAVEMENT WE NEVER NOTICED CROSSING A HOLD SHORT LINE. THE CAPT WAS ON DAY 6 OF WORKING A RESERVE LINE AND THE FO WAS ON DAY 1. THE TRIP WAS A CDO (CONTINUOUS DUTY OVERNIGHT) WHERE WE GOT TO THE HOTEL AND HAD TO WAKE 5 HRS AND 20 MINS LATER FOR A VAN. I WAS TIRED BUT FELT FIT TO FLY DESPITE SWITCHING FROM 4 DAYS OF EARLY SHOWS TO A LATE RELEASE TO A LATE SHOW AND EARLY RELEASE (CAPT). I FEEL THAT THE ADDITION OF HOLD SHORT LIGHTS AND A HOLD SHORT BAR WOULD HAVE PREVENTED THIS. ALSO MARKING TXWY C AND RWY 4/22 AS A HOT SPOT WOULD HAVE GIVEN US SOME WARNING. I ALSO FEEL THAT BEING ON A CDO AFTER WORKING A NORMAL SCHEDULE HAD MADE ME MORE TIRED THAN I HAD REALIZED. DESPITE BRIEFING THE FO ON THE TAXI ROUTING THIS MISTAKE OCCURRED; SO I ALSO FEEL THAT EXTRA CAUTION IS NEEDED WHEN THERE ARE WET SURFACES THAT MAY IMPAIR YOUR ABILITY TO SEE PAVEMENT MARKINGS.