A B737-500 TAXIED ACROSS RWY 10C AT PIT BECAUSE THE RWY MARKING WERE OBSCURED BY SNOW COVERED SURFACE.

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ATIS SAID TO EXPECT DEP RWY 14; RAMP CTLR ISSUED TAXI INSTRUCTIONS TO RWY 28C. UPON CONTACT WITH GND; CLRNC CHANGED AGAIN; THEN CLRNC TO TAXI TO RWY 10C. WHILE CAPT WAS PRIMARILY RESPONSIBLE FOR EXECUTING THE CORRECT TAXI INSTRUCTIONS; FO WAS UNABLE TO BACK HIM UP AND REMAIN ORIENTED TO ENSURE COMPLIANCE BECAUSE HE WAS HEADS DOWN RECALCULATING/REENTERING MULTIPLE RWY DATA INTO THE FMC. TXWY W MARKINGS FROM THE RAMP TO RWYS 10L AND 10R ARE STRAIGHT AHEAD BLUE LIGHTS; NO RWY END IDENTIFIER LIGHTS FOR THE DISPLACED THRESHOLD RWY 10C; NO ALTERNATE FLASHING YELLOW RWY CAUTION LIGHTS. NEITHER CREW MEMBER WAS AWARE OF XING RWY 10C UNTIL GND CTLR ADVISED CREW THAT OUR ACFT HAD ALREADY CROSSED RWY 10C. WITH THE CONCURRENCE OF GND CTLR A 180 DEG TURN WAS MADE AND SUBSEQUENT TKOF CLRNC WAS RECEIVED FOR XX PIT DIRECT IAH. UNFAMILIARITY WITH ARPT LAYOUT; AND VIRTUALLY NON- EXISTENT RWY MARKINGS WERE THE PRIMARY FACTORS IN THIS INCIDENT. THERE WAS APPARENTLY NO CONFLICT WITH OTHER ACFT CREATED BY THIS INCIDENT.