AN LJ60 CREW; AFTER LNDG AT PSP; MISSED THE TURN ONTO THE PARALLEL TXWY AS INSTRUCTED AND CROSSED THE PARALLEL RWY.

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WE LANDED ON RWY 31L (WHICH IS 10000 FT LONG). WHILE STILL ROLLING OUT ON THE RWY; TWR AID 'R TURN 150; WHERE ARE YOU PARKING?' I RESPONDED (ACTING AS COPLT) 'CARRIER X' AND THEY REPLIED; 'R ON TXWY C; TAXI SEBOUND; CONTACT GND POINT NINER.' AT THIS TIME THE CAPT WAS STILL TAXIING CLR OF THE RWY. I READ BACK THE CLRNC. (THE NEXT SEQUENCE OF EVENTS HAPPENED IN UNDER 10 SECONDS IN A TAXI SPAN OF A COUPLE ACFT LENGTHS. BY THIS TIME; WE WERE CLR OF THE HOLD SHORT LINE AND PRACTICALLY ON TXWY C (VERY SHORT INTXN). WE WERE STILL ROLLING SINCE WE WERE CLRED TO TAXI AND THE CAPT SAID 'CLR ON THE R?' I LOOKED R (I THOUGHT HE WAS TURNING R) AND SAID 'CLR R.' I REACHED UP TO SWITCH TO GND. THE GND PERSON WAS TALKING TO SOMEONE; SO I REACHED DOWN AND SWITCHED OFF THE RECOGNITION; STROBE; AND LNDG LIGHTS. I REALIZED WE DIDN'T TURN AND LOOKED BACK UP (ONLY 2 SECONDS LATER); AND I SAW A RWY IN FRONT OF US. (I BELIEVE MY THOUGHT PROCESS WAS; HE THINKS THAT RWY IS CHARLIE AND HE IS GOING TO TURN R ON IT.) I SAID 'THAT'S A RWY.' THE CAPT SAID; 'YEAH; CHARLIE IS ON THE OTHER SIDE.' BEFORE I COULD PROCESS THIS; WE WERE ACROSS THE HOLD SHORT LINE AND ROLLING ACROSS THE RWY. I WAS AWARE WE WERE IN THE WRONG PLACE; BUT NOW FELT THE ONLY THING TO DO WAS TO CONTINUE ACROSS AND GET CLR. IT WAS TOO LATE TO STOP. ONCE ACROSS; THE CAPT KEYED UP GND AND BEGAN TO TALK TO THE CTLRS. THEY GAVE US A PHONE NUMBER FOR A POSSIBLE PLTDEV. THE CTLRS THEN CLRED US TO THE RAMP. WE THEN COMPLETED THE AFTER LNDG CHKLIST ON THE WAY TO THE RAMP. AFTER DISEMBARKING OUR PAX; THE CAPT WENT INSIDE TO MAKE PHONE CALLS. HE THEN CAME OUT TO THE AIRPLANE AND I OVERHEARD HIM DISCUSSING WITH OUR CHIEF PLT THE POSSIBILITY OF TAKING A RIDE DOWN TO THE INTXN TO LOOK AT IT. THE CAPT THEN ATTEMPTED TO CALL BACK THE PERSON WHO HAD OFFERED THIS TO HIM EARLIER. HOWEVER; FOR SOME REASON; THIS COULDN'T BE ARRANGED. THE CAPT DECIDED TO HEAD BACK TO HOME. I HOPPED UP FRONT AND CALLED FOR OUR CLRNC. THE CAPT THEN STARTED THE ENGS. WHILE SITTING IN THE CHOCKS; A WHITE ARPT OPS TRUCK DROVE BY AND DOWN TOWARDS THE INTXN IN QUESTION. WHILE TAXIING OUT TO RWY 13R FOR DEP; WE WENT BY THE EXACT INTXN WE HAD BEEN AT. THERE IS NO CHARLIE SIGN NW OR E OF TXWY C. NOTHING; ON WHAT WOULD HAVE BEEN THE CAPT'S SIDE; IN FRONT OF US OR AT RWY 13L/TXWY J WHERE WE HAD THE INCURSION (DESPITE A BLANK SIGN ON THE SE OF TXWY J/TXWY C AT RWY 13L). THE SIGN SAYS 'J/13L' BUT NOTHING ABOUT BEING 'ON' TXWY C.