A PA32 PLT TAXIED WRONG DIRECTION AND CROSSED AN ACTIVE RWY WITHOUT A CLRNC.

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I WAS INSTRUCTED BY GND TO TAXI FROM FBO TO RWY 36C VIA TXWYS C; E; AND J. I WAS UNFAMILIAR WITH THE ARPT; AND NEW TO THE ACFT; HAVING JUST BOUGHT IT. I HAD A TXWY MAP IN MY LAP AT THE TIME. MY ERROR WAS TO TAKE A L ONTO TXWY C RATHER THAN A R. THAT TOOK ME ACROSS RWY 27 INTO A CONSTRUCTION ZONE. WHEN I REALIZED MY ERROR; GND INSTRUCTED ME TO REVERSE COURSE AND CALL THE SUPVR. HE TOLD ME THAT RWY 27 WAS OFFICIALLY ACTIVE AT THE TIME; ALTHOUGH I OBSERVED NO OPS FROM THAT RWY. TO PREVENT SUCH INCIDENTS IN THE FUTURE; I WILL ALWAYS ASK FOR A FULL PROGRESSIVE CLRNC WHEN AT AN UNFAMILIAR ARPT; AND WILL NOT CROSS ANY RWYS UNLESS EXPLICITLY TOLD TO DO SO. HAD I REQUESTED A PROGRESSIVE THE INCIDENT WOULD NOT HAVE OCCURRED. I AM FROM THE NE; AND AM OFTEN TOLD TO TAXI VIA RTES THAT TAKE ME ACROSS RWYS. I OFTEN CALL BACK TO REQUEST CONFIRMATION THAT I CAN CROSS THE RWY. I SHOULD HAVE DONE SO THIS DAY; BUT PERHAPS INHIBITED FROM DOING SO BECAUSE THE FREQ WAS SO BUSY. THE ERROR WAS CERTAINLY MINE. ANOTHER WAY TO PREVENT THESE INCIDENTS WOULD BE TO MAKE IT A RULE THAT ANY TIME A RWY IS TO BE CROSSED; GND WILL EITHER SAY TO HOLD SHORT; OR GIVE EXPLICIT INSTRUCTIONS TO CROSS. IF THERE WERE AN ABSOLUTE RULE THAT THIS IS ALWAYS DONE; THAT ANY RWY ALONG THE TAXI RTE WILL BE MENTIONED EITHER AS A 'PROCEED ACROSS' OR AS A 'HOLD SHORT OF;' I WOULD HAVE REALIZED MY ERROR BEFORE XING RWY 27 AND WOULD HAVE CALLED FOR CLARIFICATION.